Tell us about yourself!
The LEDs your looking for are likely WS2811 or WS2812. If your wanting to just flip a switch and have it start its sequence, an arduino running a program with fastLED or neopixel library will be able to handle the 150 lights without an issue.Where this is going to get more complicated is the battery. I usually figure an average use of 1.5 amps / 50 lights, so your talking roughly 4,500 mAh per hour you plan on running this.
I did something very similar for an entire Christmas tree, I have 2 suggestions to help a bit. 1) get a few inches of 1/4" square copper tubing and heat the end with a lighter/torch and use that to cut the hole in the ping pong ball. Its cleaner and much faster. i was able to do around 100 in 10 minutes.2) buy much cheaper ping pong balls (like these https://www.amazon.com/dp/B01IEB5T2U) the cheaper ones don't need to have the writing scrubbed off, and have an actual seam on them so you don't get that dim band around the ball where they overlapped the shell to be smooth.cool to see this up here though using the same LED boards i used.
"Brick and Mortar" Cutting Board
Make a Massironi shelf
I created an account just to give a shout out to your clear acrylic & velum solution for the diffuser. I experimented with different white acrylic thicknesses, and different vinyl frosting solutions and wasn't happy with the result. after testing a $0.60 piece of this stuff, i was so pleased i tore apart both of my 512 light versions to replace them with this.