@AnasMalas
I'd love to see how you plan to connect up a many-pin MCU, a many-pin shift register, 15 LEDs, a power supply and control switches, without using a printed circuit board or a breadboard.
I agree that using a ProMini might be a good solution since you don't want RGB addressable LEDs (which are also available in through-hole leaded packages of course, for a bit higher cost), but you will still have to do some programming and soldering. You'll have to have one FTDI programming module in order to program the ProMinis. You'll have to learn how to multiplex the PWM outputs to be able to control all your LEDs, and you will likely have to use external transistors to drive the multiplexed LEDs to acceptable brightness. The ProMini will still require a power supply and control switches. The LEDs will still require some kind of mounting arrangement, and if your friends want to "swap them out" for some reason you'll need to provide some means for doing that. Will they be soldering them? To what?
And will a <$4.00 Chinese clone ProMini actually work properly? I use ProMinis in my own projects but I've never tried one of the cheap clones, so I can't speak as to their reliability. (I do have two projects with genuine ProMinis that are running constantly in my lab (a color organ with 12 LEDs and a multicolor flasher with 1 RGB LED) and have run for several years continuously without problems. I also have that NeoPixel demonstration box, now using a single ProMini that is controlling 2 NeoPixel rings, one 24-LED unit and one 16-LED unit, for a total of 40 RGB LEDs, with color and brightness controlled by software.)
Please understand that I am trying to help you figure out the easiest, least expensive way to get to your final product as you've described it.