A CO2 laser with abit of power, <100watts, will mark stainless steel provided Oxygen assist gas is used.
Laser marking onto stainless, without a marking compound, is oxidizing the surface. <= a process called annealing. (As opposed to engraving, which is removal of the material)
You are basically drawing the carbon in the stainless to the surface, creating contrast. Therefore the resultant mark is prone to rusting if left bare.
Always consider the end use your products before making the decision. It may be that a marking compound will be the better choice.
And although RPosty is on the right track, a 'good' Nd:YAG laser marker will have a closed loop water circuit (not allowing air entry) and will have a deionizing filter with conductivity measuring circuit to prevent flash lamp from firing until the water conductivity falls within preset levels. It will take longer the more the machine has sat idle.
But you should be flushing at least yearly. (same for anything with a flush button.

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Go fiber, galvo system if mark size is small enough, xy if not. (or a combo system)
Small, no chiller, low power requirement, plug into wall, usb or ethernet/wifi to pc, and away you go.