Apologies for not having more detailed images... I don't have a good setup for photography while using both hands.

Add some new solder to each of the three terminals on one microswitch.

While pulling the microswitch away from the board, heat its three terminals. The switch should come free.

If you have trouble with this method, you may have better luck by removing as much solder as possible using solder wick and a solder sucker before pulling the microswitch away. However you do it, all three terminals will need to be warm enough to melt their solder at the same time.

Clean the terminals of any excess solder using a solder sucker and solder braid. The holes in the board should be clearly visible, it should be easy to insert your new switches.

Double check to make sure each solder pad on the bottom of the circuit board has continuity to the trace surrounding its corresponding hole on the top of the circuit board in case you separated them while extracting the old switch.

Repeat these steps for the other microswitch.