First of all, don't assume that you cannot use the VEX transmitter and receiver. Although I can't find this year's Skills Canada rules on line anywhere, I have read them and they seem pretty similar
to last years. Page 14 specifies ground frequency transmitters OR the Spektrum, and I believe this year's rules are the same. The VEX transmitter and receiver use ground frequencies.
The real catch, however, is that as you say the VEX cpu is probably not allowed as it would likely constitute a "complete, out of the box" system, specifically disallowed under Skills Canada rules. This is where knowing, for sure, that a STAMP or Arduino is allowed would come in handy. (This might sound odd for those used to FIRST competitions, but Skills Canada works under the "student designed-student built" philosophy, has no KOP and specifically disallows teachers and mentors from entering the pit area for instance.)
But don't count my advice as to the rules... ask a question of the organizing committee... can you use the VEX Transmitter and Receiver? Can you use the VEX Transmitter and Receiver and CPU? Can you use the VEX CPU by itself? How about a BASIC Stamp or an Arduino (they might be allowed as a general purpose board, rather than a complete out-of-the-box solution)?
If the answer is, as you suspect it may be, "No" to all of the VEX related questions above, then you will probably have to come up with your own control system. The important thing for us to know in order to help you is what functions do you want the controller to have? There is no autonomous component to the competition, and most Skills robots are directly radio control... sometimes complemented with an on-board controller that responds to onboard sensors, as opposed to responding to the remote control inputs.
So check out what you are allowed, and give us a better idea of what you specifically want to do.
Jason