If the LA refuse to assess because they say there is no proof of SEN appealing that if you have to take it all the way to tribunal is months. I just had 11 months wait for tribunal after the LA dragged their feet the full allotment of time to get to mediation. Then you win because the law is may have SEN, tribunal orders the LA to do the EHCPNA which they have 20 weeks to do from the date the order is written up. My order took 4 weeks. Most LAs are going over the 20 weeks regularly too as there is a national shortage of EPs. So by quoting the LA legal obligations and arguing your child has SEN you can save over a year of time a child is without adequate support for the education they are legally entitled to. Then the EHCP may not be fit for purpose with lots of wriggle room for the LA to get out of providing so in real terms the child isn't getting the support. Then you either go back to tribunal over the contents of the plan- again this process is near enough a year in at least some areas. Or you fight it out at the annual review which you may not be offered and also have to make formal complaints to get (routine occurrence in mine and neighbouring LA).
It may be true that you don't technically have to argue your child has Sen. It may be true that the LA should do the EHCP needs assessment to determine the needs rather than declining because they say no evidence of needs. But the reality is if you start the process countering this common LA delay tactic you can save the child a year+ of inadequate education.
OP I would use the reports you have from school about your child's academic level as 'evidence' of SEN. The support plans in place for the support he currently receives. If the dyslexia diagnosis is official use that too if not then the screening the school did or any emails you have where teachers raise concerns around dyslexia. Read up on the assessment criteria and join your local Facebook send page and read others stories locally of your LAs tactics. try to preempt the LA reasons for refusal before they make them so hopefully they accept the application without having to go to tribunal etc.
This is a long process and won't be done in time for senior school. You said you planned to see how he gets on. I think that's wise. If he can't cope you are not faced with just the two options of leave him in school while the EHCP cogs turn or pull him out to home educate. You may be told if you withdraw him then the LA don't have to provide EHCP. It is true technically if you withdraw him you become responsible for his education and the LA don't have to fund or provide sen support. I got around this by arguing I'm not willingly withdrawing my child, this was not my choice it was the best way to meet my legal obligations as a parent. I can't remember the law but there are multiple parts you can quote. The main one is actually relevant to home edders ALL parents have a legal responsibility to ensure their children get an appropriate education either by attending school or otherwise. You can argue the school is not appropriate and by sending your child you break your legal responsibility. You also break your legal responsibility to protect your child from harm by knowledge sending them to a school you know will de emotional damage (again I can't remember exact phrasing and the acts are long it's late I'm not reading them to get the reference now). If you argue this the LA have no defence and will have to continue the EHCP needs assessment or tribunal. Then after a certain number of days you can argue the school or LA need to provide alternative provision or some form of edit while your child is out of school. Again there is a law you will have to quote likely in a formal complaint. I want to say its 20 days out of school but not sure. This is another fight you may not want to face but it's an option you should be aware off.
I know loads of families who gave up on EHCP as it's a stressful process and just home educate. I know quite a few who got the EHCP and still end up home educating either because the provision was still inadequate or while they wanted in a Sen school place. So you may not want to even start the EHCP fight. I just personally feel it's better to fight the LA over your kids education than have the fight be with a child who struggles, who you don't have the skills ti support and who subsequently resists your teaching. The LA will check you are proving a suitable education. Arguing with them over what is suitable for your child is also very stressful.
And I'm absolutely not saying you cannot support your child so absolutely should not home educate. I don't know you I can't judge. I'm speaking from my own experience home educating two very different children, one is out of school due to anxiety and struggles surrounding her autism. She does not have significant LD, im paying for her to have dyslexia assessment as everyone else in the family has it and she's got traits. But she is not 'behind'. My other child is significantly behind, still can't really read or write. He should be year 3 but working at reception level. It's completely different educating him at home the stress of it has been so damaging to our relationship. He make minimal progress even with a fair bit of "alternative provision" and tutor hours I got for him while we waited on the tribunal. Because his education isn't my responsibility I have not been penalised for his lack of progress. I have a friend with a similar child who is being taken to court to put her child back into school (without support in mainstream) because she cannot evidence progress enough to satisfy the LA home education person. There is a real drive for further monitoring of home education it is very hard for us home educating kids with LD to meet the requirements. My dd who is academically able is easy to write the reports and show progress, I don't feel aweful when I say no screens till the work is done etc because I know her resistance is because she doesn't want to not because it's so hard for her it's causing such distress as is the case for my boy.
You know your kid and what your relationship can take. Just think it through. And good luck