The Home Depot's in the U.S. have a tool rental section. Check there to see if they have the setup. Another alternative (which I personally prefer, but some may poo-poo) in the tool rental section is a dedicated biscuit cutter. The biscuit cutter should come with it's own blade, so the only cost associated with that should be the rental itself.
For what you're looking to do, you should be able to get the rental fee a step below the daily rate. Prolly around $15-25 for the time you'll need it.
If you're gonna go the "cut the spline off and glue it" method, get some epoxy to do it, since you'll need this to be fastened better than the "normal" way.
You could nail/staple it on, but if you go that way, I say why even bother with doing it?
One last option requires a nail gun OR a nailset and patience. Cut a trim piece of hardwood/softwood and nail it in place. You'll only be able to finish it square (flush) or use a saw to angle it so it'll have a "V" to it. Use some finish nails, either using a nail gun, or a nailset to set the head flush/below the surface, and you're set.
Other than those options, I believe you're SOL.