Replace $1 ||$2 with $+. That'll contain the value of the last capture that actually matched. See perlvar:

The text matched by the last bracket of the last successful search pattern. This is useful if you don't know which one of a set of alternative patterns matched.

p.s. Originally I mistakingly had posted this as a followup to Re^2: How do I avoid double substitution when replacing many patterns?, now its sibling.