Could I use an LM317 regulator for each board to deliver precise voltage?Yes.
If you don't have a multimeter, I suggest you get one to confirm the voltage before connecting the audio circuit.
Are transistors necessary?No.
The LM317 can put-out something like 1 Amp, which is more than you'll be "pulling" from a typical small battery in a toy. (I don't ahve the spec sheet in front of me, but it depends on the voltage "dropped across" it and heatsinking, etc.)
Can the output of the boards be wired to a single amplifier circuit?No!!!
The general rule is that it's OK to connect two or more inputs
together (such as connecting multiple amplifiers), but you should NEVER connect outputs together.
For audio applications, you need a "mixer". In this situation, you can make a passive mixer with some equal-value resistors (1k to 10k should work). Connect a resistor to each output, and connect the other ends of all resistors together and to the amplifier input. With a passive/resistive mixer, there will be signal loss. If this is a problem, you can build a summing amplifier
with an op-amp.