Yes, what you want to do will work.
I would cut the 12V PC wire (yellow = 12V, Black = ground), strip the ends.
Then do the same with the power wires for the coin receptor. Go to AutoZone, Pep Boys, Advanced Auto parts, any auto parts place near you, and buy a pack of the male/female plug connectors. There are several kinds to choose from, pick one that works for what you like. If you do not have the correct wire crimping tool, use a good pair of pliers and squeeze the crap out of it. Ensure you always pull on the wire and the crimped end to see if it will separate. The harder you pull and it does not separate, the better connection.
I am pretty sure I have the colors correct, if not use the Red.
From my experience, when dealing with any type of electrical equipment where you may need to separate the equipment from the power supply, always do so using a means to "un-plug" the connection.
Cover all that up with electrical tape if you want.
Good luck.