Assuming the failing units are not seized, a person should be able to easily check this by applying power to the fan and observing the signal present on the remaining lead(s); a likely third option is that this is a speed control input; if four wires are present, one is likely speed control and the other non-power lead either tach or locked rotor sensor. A description of common DC fan signals can be found here.
Substituting a fan with locked-rotor feedback for one with a tach signal (or vice-versa) will not necessarily result in damage, though it may also not work or not work properly depending on how said signal is used. Fan failures in improperly protected equipment can result in damage due to overheating, and it’s conceivable that a replacement fan drawing more power than the original could cause damage to the fan drive circuit, though within reason this seems an unlikely result to me.
Best bet would be to do a bit of homework/measurement and find something that’s as close a match as possible.