OP, i've been in your exact situation. Eventually, i moved schools.
We were also in Scotland but at the upper end of primary school. Neither my child or the other had a CSP just a standard 'additional learning support' programme. Due to cuts in the local authority, there was only one TA for the entire school. No child had 1:1 time.
My child does not have violent outbursts but does require a lot of support to help focus on class work and to join in group work.
The other child was extremely violent and took up almost all of the teacher's time or the head teacher's time. My child was getting no additional support due to lack of resources and other children were also being deprived of education.
This other child would hit other children and staff at every opportunity. I knew the parents and they were dead set against applying for a place at the specialised school as they wanted to stay in mainstream (their right). Me and other parents complained to the HT about our children being at risk and being constantly exposed to violent behaviour. The HT wrote a letter to us all stating that due to funding cuts, the school were facing a crisis in regards to adequate staffing and resources and called for parent volunteers to come in to work with the children.
Absolutely appalling.
Thankfully, we have since moved and my child is now getting 1:1 time with a TA for about 6 hours a week outside of the classroom. Such a better experience.
I'm still in touch with previous school parents and the situation is no different over a year later. There is still no TAs and, although there are some parent volunteers in the class now, the teacher still spends most of her time sitting with the other child and being hit on a daily basis.
I know it's absolutely awful to say you do not want your child to be in the same teaching environment as another child with significant additional needs. But - you need to think of your own child first and foremost. Based on my own experience, your child will not have her needs met if there aren't any TAs or additional resources in place. Your child is likely to become desensitised to violent behaviours and swearing on a daily basis. Your child will expect to be hit, bit or see her friends/teacher hit or bit or sworn at on a daily basis. Your child will not bother asking the teacher for help because she'll learn to know that the teacher is too busy with the other child. Her self confidence and her learning will suffer as a result.
Moving schools (and moving to an area that hasn't yet been hit by such cuts) has been lifechanging for us. My child is no so happy and getting so many more opportunities than before.
If you're not keen on moving schools, give it a go first and see how things go until the October break. Then reevaluate the situation.
Don't let anybody make you feel guilty for thinking of your own child's needs before this other child's. He/she has his own parents to think of him first.