JeanB - Yes, to some extent. I don't like it, but it can be made to work:-

The relay board is low-side switched, so the existing 0V through the micro-switches to the 3 inputs (X/Y/Z) would work. You have to provide a 5V supply to the relay board as well, likely rated around 250mA for 3 relays.

The relays are change-over contacts, so connect +5V to the NO contact, and 0V to the NC contact and use the pole contact(s) as the drive into the controller card. That way the contact is either connected to +5V or to 0V, without any floating or high-z input resistance at play. The optoisolator input requires a good few milliamps and I think it unlikely to be as susceptible to noise.

The problem this does introduce is switching time (but not really important) and contact bounce (when the relay switches for a couple of milliseconds). Again, I don't think this is going to be important.

The bit I said about about NO/NC contacts being +5/0V - can't be arsed working out which way around - try and see. But if you want to change the microswitches from NO to NC then just swap the NO/NC contacts on the relays to match.