I don't think that there is anything, short of actually being commissioned, which will stop the DS at Sandhurst from shouting at you.
As for haircuts, turn up with a neat 'short back and sides' and you will be OK. I would predict a relatively hard time for anyone turning up with a 'No 2 all over' as the DS will suggest that it isn't terribly 'officer-like'. Dunno if they still do it, but we all got a savaging from the Academy barber in the first couple of days which rendered the haircut we'd arrived in irrelevant.
Sandhurst is certainly not the place to play the grey man, but conversely, making a big effort to get noticed on the first day would be a mistake!
If you are planning to have a holiday in the sun before going to Sandhurst, I suggest you get your cut before you go on holiday. When I went to Dartmouth one of my colleagues ended up with a pale white line all round his hairline after the college barber had got to him.
When I was there we had one of the guys on the course with alapeccia ('scuse spelling - not a hair on his entire body) and they still made him sit in front of the barber and pay the man for a `haircut`. Everybody got one!!
Can you confirm you're still going? Not planning for Jan myself but we've been told it's been cancelled. If not, might be worth letting the lads know so they can ask the powers that be to find out for them.