Let me look closer.
REGEXP is probably more resource intensive than LIKE for sure, but I'll bet it is less intensive than 2-3 LIKES.

I Managed a server that did a lot of REGEXP on datasets of up to 10,000 records withing a query set that had to be exanined, with some 200-800 queries per second, so unless your even within 20% of that even on a sared server, I don't think it will be noticable.

I'll get back on this