Limits, homes, override switch

[JAZZCNC]

I could share the job on the same switches, but the relay implies some risky delay (are miliseconds really that risk JAZZ ? That's where I'm not too sure...).

Not case of being risky. It's case of not being repeatable. The whole point of HOME switches is to be able to repeatabily return to Fixed position every time. The random delay between when switch is triggered and time takes relay to open it's contacts to allow message to control makes repeatabilty impossible.
The delay for limits isn't so important because like you say it's milliseconds but for repeatabilty purposes that is life time plus it's random amount of time.

I'll order three more switches online for the sake of completeness of the machine, but I'll use it without homes until they arrive. Now, can you tell me what kind of switches I should get ? Laser or same type of mechanical switch ?

Again because of repeatabilty you wan't slightly better switch for homes. Personally I like using inductive Proximity sensors because they are accurate and repeatable. Well more than enough for router anyway.