Master degree in EE here. It will almost certainly be fine to swap those batteries like that, I would be more cautious if it was some cheap Temu device but for a vintage Yamaha you'll be fine.

One thing I will caution you about though, the synth almost certainly lacks under-voltage protection and could drain your 18650s below their minimum voltage. Make sure your cells have built-in protection or add some of your own.

Lithium batteries are a bit finicky, they self-discharge, and the rate varies from cell to cell, so if you have three cells in series at 4V, some of them will drop in voltage faster than the others over time

When you then charge them in series like that, it'll charge until the three cells combined are at 12V, but that might mean that one is at 4V, the second is 3.9V, and the last is 4.1V

This drift keeps happening over time, and eventually one cell will end up at a dangerously high voltage, potentially catching fire

That's why with lithium batteries, you need a monitoring circuit that keeps the voltages of the cells balanced

So i would not advice you to simply swap them in like that, you could charge the cells in an external charger and then use them in the device, but remove or isolate the 12V supply (add a diode to the batteries so power can go out of the cells, but not go back in) so it doesn't charge them while installed

NiMH batteries might be a better fit, they basically self-balance i believe, but you'd need 10 cells in series to reach 12V

Edit: completely missed the switch there, yeah 18650 cells charged externally will likely be fine, they are usually charged to 4.2V, so 12.6V total, the regulator is likely rated higher than that

If you can I would open it up, find the voltage regulator, then look up its specs. 12.6v might be pushing it a bit but still within spec. Adding a little heatsink if it can fit would set you up a lot better to then run 12.6v frequently.