Can a power cable from an AC adapter be safely split into separate wires?
First of all, don't tamper with AC. Just making sure. My answer is talking about the DC side, which in this case is 12v and classified as "LVDC", a low enough voltage that is safe to work with.

On to your question, yes, this idea will work. At least when using multiple-pin connectors, this is called "current sharing". You can think of each wire being a resistor, with (in this example) one resistor being replaced by 4 in parallel. There will not be a problem, as long as the resistors are more or less equal.

This can become a problem (usually in larger loads, or with extremely small conductors) if your resistance in one of the four resistors starts going up (for example, is completely disconnected, heats up or is broken.). In a vicious cycle commonly called "thermal runaway", you can end up having more current on the individual wires than they can safely handle, thus heating them up, and having their resistance go up, or even melt themselves.

-Source: EE student and designer, have done this myself on multiple occasions, also fried many LED's due to unstable current sharing.