The hardware restrictions of the earliest IDE HD based MP3 players really have nothing to do with any limitations on modern shuffle ability.
IPod in 2001 had 32MB of RAM. 2k RAM is not relevant to this discussion. You getting close to discussing 3 decade old technology.
Using random number generators for shuffle mode was a stopgap measure that everyone else cargo culted because it's easier than critical thought.
So how about using a maximal linear feedback shift register of smallest size greater than the number of songs, skipping entries that are beyond the end of the list?
Either keep the polynomials[1] in a small list, or implement them as separate functions, invoking the one you need via a function pointer. Both approaches take just a wee bit of extra FLASH/ROM, and just a few bytes of RAM.
https://en.wikipedia.org/wiki/Linear-feedback_shift_register...