Firstly, some mainstream secondaries have excellent SEN departments and will organise the transition for you, and put the help in place afterwards, it is to their advantage to give your child help once their needs are recognised.
Some EHCPs guarantee the schools no extra money, or at the least the LA s may resist topping up the EHCP with any extra funding, despite what the specified help is (this game of passing the buck may go on for many many months)
So if you can define what your child's needs are to the Secondary, and they show signs of "listening" and tell you what the tailored support is, you may not need that EHCP.
Before my ds2 applied for secondary I emailed every SEN department in turn and asked them how they would help my son. The school that gave the best response ended up as our first choice for ds, and they certainly organised a very good transition for him, AND a taster day for a TA supporting him a year 7 class when he was in Year 6.
In the event, it all went a bit pearshaped because his dyslexia was so bad and the homework was not really differentiated, but they did accommodate him enormously, include him in all sorts of extra curricular activities, put a TA in to support him, the SEN head was always there to listen to problems, and I suspect they would have given him a differentiated homework timetable if I had flagged it up earlier as a source of severe anxiety.
However, what I would say, is that the lack of any clear definition of his exact needs was what made things difficult for ds.(and why we ended up home educating him and applying ultimately for an EHCP to change schools) He did seem to cope with things and be "clever" but the thing they couldn't anticipate what his anxiety about Year 7 tasks because he couldnt cope with socialising. The EHCP itself may be the only way to get a clear picture of what your child does need, in turns of OT, language and communication and comprehension.
You are likely to be turned down, because most requests for assessment are, that is just the game they play, but you can use your evidence to apply for the secondary that you think best, and the evidence that you applied for an EHCP in itself.
The most important thing I think is just to find a good secondary that will be supportive. They will be supporting children with and without EHCP plans who have SEN, and it is not necessarily the case that they get any more money to support the ones who have EHCPs any more.