Can you? Sure.
Should you? Depends on what you mean by a "racing" air filter. There is not really any such thing.
For example, the air filter in my "racing" motorcycle, that really is used for roadracing, is an original-equipment Yamaha air filter for that bike. Reason: there is nothing to be gained by using K&N-type filters (don't believe the marketing hype) and they let in more dirt, which would wear the engine out sooner. There are some cases where the K&N oiled-cotton filter will make less power than with a stock air filter.
As for reprogramming, normally any differences that might exist due to a different type of air filter will be so small as to make no difference.