Yes, you can use this switch.
You can mount it in this hole (see red arrow).
No plates for installation, because it is designed to be soldered to the board.
Maybe you should mount it on universal pcb (like this) and fasten it somehow to the boombox case....
Another option is to seek a similar switch by some old junk electronic components - TV, radio, tape recorders ....
Is there a store in your town, where sell such electronic parts and components?
---