If someone's got an aspirin allergy, it means that he or she is sensitive to any form of leukotriene overproduction (diagram in FA illustrates well how COX inhibition shuttles substrates to the leukotriene pathway).
I would assume that irreversible inhibition with aspirin would be the worst, followed by that seen with a reversible, potent NSAID (e.g. indomethacin), then possibly, last on the list, that seen with a COX-2 inhibitor.
I've never heard of specifically not prescribing an NSAID to a person who's had a history of aspirin-induced asthma or HS / rash, but it just makes sense that you wouldn't.
For instance, if a 68F diabetic with malignant otitis externa (i.e. P. aeruginosa) has had a Hx of penicillin allergy, you probably wouldn't want to give her ceftazidime, knowing that she could be allergenic (10%), when you could just give her aztreonam.
If someone has a Hx of aspirin allergy, don't give an NSAID. It's just better medicine.