DS won't use the toilet at nursery

[MumOfAToddler26]

DS is 3.5 and currently doing a couple of mornings (3.5 hours) a week and won't go to the toilet at nursery.
It's not a big deal as he is only there for a few hours so he goes as soon as we get home. But after Christmas he will be doing a full day so he will have to go.
When I said to him about it he gets upset saying he just wants to wait until he gets home to go for a wee, and I said why? He said because I don't want anyone seeing my Willy 😂
Is this a common thing and has anyone had any ways to over come this?
I said well just go to the toilet and ask the ladies to turn around while you do a wee, the thing is he can pull his pants and trousers down himself and go for a wee on his own but struggles to comfortably pull them back up again so would need help making sure they were pulled up properly.

I wouldn't go at preschool as a child, thankfully only did mornings, my mother did have to get me straight home. When I started school I didnt like the loos and it caused me to spend a whole term crying at drop off. I can still remember all the details of the loos over 30 years later.
I did eventually overcome the crying but I'm still picky about loos. As I was there all day I had to use the loos so that was that.