Go to
Amazon and search "battery powered LED light strips" and you'll get a ton of results. Unless your husband or someone you know is good at wiring the lights to the scooters battery, and adding a separate power switch so it wouldn't drain the scooter battery down accidently, I'd make sure you stay with LED's that come with their own power source. A lot of them just take AA batteries, and come with either a wired or wireless remote to control the color patterns and all the different modes.
You'll quickly notice on Amazon, that they come in short lengths, and extremely long lengths, but a lot of them are cuttable, and also make sure they say for indoor / outdoor use. If you don't want to mess around with cutting, use a flexible tape measure for sewing, that will help you figure out the pre-made lengths you might want. A lot of them come with tape on the back of the strip, you just have to peel it off and could possibly stick them right on the plastic covers or wherever there's a good spot on a scooter. That's more of a permanent mounting approach though, so you might want to use smaller pieces of double sided tape or velcro tape to make removing the strips easier if this ends up being just temporary. We just used different size wire ties / zip ties to hold the strips to parts of my wheelchair.
I'm by no means an expert with these strips, we have a Polaris RZR 4 seat side by side and DH added two LED whips and LED rock lights under ours, which are made with the same components that you can get on Amazon. The whips just have a clear shatter proof tube around the LED's to protect them from tree branches and other stuff while riding.
Several years ago we went to a Halloween party, and DH and I dressed up as Tron characters. So naturally DH had to wrap the LED strips around my wheelchair frame, footplate, backrest, and wheels. He used 3 different light sets, so my wheels had one small strip each, and my frame, back rest, and footplate had one longer set, all 3 could be set to different colors, or modes, but I kept everything the same for the most part to keep the Tron vibe. My chair was a far cry from looking like an actual Tron cycle, but it sure had its own cool factor, and everyone loved it and our costumes that also lit up. I'll see if I can find pics from that night, it was years ago, and I don't know if they're still on FB or one of my friends Instagram pages.
Good luck, and my advice is don't feel like you guys have to go over the top right away, just get a strip that's a few feet long, and have fun experimenting with that first.

Please feel free to ask me any questions.