Generally, those color-strips use RGBW LEDs and have chips controlling each LED’s color, which you control via a little pad-thingy or whatever to pick the color(s) you want, patterns, etc.
Dunno if you want a static display of just multi-color LEDs, or want to cycle through colors, patterns, etc.
If you want to go the chip route, you may not have a choice but to feed it the voltage it wants.
Ever consider those LED strips that go on bicycle spokes, to show pictures, patterns, etc., as you ride? Should be more compact, and a more reasonable power supply.