You could probably increase the fuse size to include the light strip (obviously to a very specific amount), as if anything actually went awry it would still be the same kind of safety at the proper level, just plus accounting for the light strip, if that is easy to understand - the range between "healthy" and "there's a problem, fuse needs to blow" would still be the same as long as the light strip was pulling a load and taking any of the extra free space you've given that a malfunction could abuse without it. You'd just have to remember to change the fuse back if you ever removed the light strip from the cabinet.

That being said though, not sure how the power supply, connectors, or wiring would like that though - so the external power supply is probably your best bet.