3 way selector switch to Push Button switch
Yes, you could replace it with momentary switches but it's not simple. That is a 3 Pole 3 Throw switch. For a push button you would need at least three 3 pole Single Throw switches, one per input, preferably ones that are ganged together (so pressing one disconnects the other). And if its momentary you would have to hold the button in for it to work. Or you would need to replace the switches with analog control circuits to switch the inputs. Or a digital circuit with bus switch ICs and microcontroller.

It's so much easier to buy one that does what you want. There are super cheap ones with remote controls even!