I think the school is being U re: timescale - I'm a governor at a primary school , and we notified parents of
the last uniform change several months before the new uniform should be worn (just before Summer Term half-term break in readiness for new school year in September). But at the end of the day - their uniform, their rules.
You could send your DS in in the "wrong" shoes, but bear in mind this could disrupt his education (sent home to change shoes, etc), get him hassle off teachers, or lead to more severe sanctions.
But PLEASE, OP, whatever you do, don't do what my Mum did(twice!):
I started secondary school just after my older sister had just left school completely (not the same school as the one I was due to attend). My Mum decided (even though my school's regulation duffel coat was grey and my sister's had been brown/camel) that she was not going to buy a new school duffel coat for me when she has my sister's which was "perfectly good". I got pulled up by teachers numerous times for having the wrong coat, but whenever I reported back to my Mum that I'd been told I had to stop wearing the "illegal" coat, she would just tell me to tell the teachers that "my Mum says she's not forking out for a new coat when I have a perfectly good duffel coat already". At the time I was 11! I basically when without a winter coat all through most of secondary school until I outgrew my sister's coat.
The second time was more like OP's example - after my 1st year at secondary school , the school changed part of the uniform, from a plain grey cardigan to a v-neck jumper with the school stripe around the neck. Again, my Mum wouldn't buy the new jumper as what I had already was" perfectly good". Again, I got endless hassle off teachers for wearing non-regulation uniform (even after my Mum took the buttons off the cardigan and sewed the front up to look like a jumper). Again when I reported back that I'd been told to stop wearing the "wrong" item of uniform, threatened with detention, etc, she told me to just tell the teachers "my Mum says...." as she had with the coat the previous year. I would have been 12/13 by this time. I just didn't wear a jumper until I grew out of the cardigans.
So, if you are intending to send him in in the wrong uniform, please be prepared to go into school and fight your own battles against the uniform change, and don't expect your DS to do it for you!