Pretty sure you're OK royalty-wise as long as there is no accompaniment and you're just singing the words and not having your skit recorded for commercial purposes.
Awhile back I bought a royalty-free music CD with hundreds (300!) of tunes on it off of eBay for $12 or $15. Several of the catchy and upbeat tunes are 30 seconds long, which is the perfect amount of bumper time for me to transition from one puppet to the next. If you do a show, it enhances the professional quality to have some bumper music between transitions, as well as introductory and closing music. And royalty-free music means there are no worries. It's a lot better than, "OK, and now I'm going to get my next character..." with 20 seconds of silence while you undress and dress your arm.
I'm performing at a large family reunion tomorrow and my 10-year-old daughter is running the CD player. It's a 25-30 minute show, but I never do even these smaller-scale shows without musical accompaniment.