I’m saying those races could work well, basically anything with an automaton could be a “Tinker” whether they use magical or mechanical means to move their “mech”.
The races I’ve listed are just the ones we’ve seen have a history with Automatons, mechs, and vehicles.
Dwarves: Known for their tanks and siege engines, and as dark irons, and earthen actually use mechanical automatons and golems quite frequently it’s not too far of a stretch.
Orcs: Adopted the Iron Horde technology we see in WoD, developed by MU Azeroth Goblins for Garrosh, again not a stretch to say they could build mechs.
Elves: Belf and NB are seen with tons of hulking automatons walking about, although they are powered by magic, they can be considered mechs as long as pilotable versions are made. Velfs understandably inherit the Belf’s automaton, except with a more Void/ethereal theme.
Forsaken are seen with a ton of sophisticated seige weaponry, blight catapults, blight tanks, etc, etc. Not too far a stretch to give them mech either, and it would look awesome thematically.
Zandilari trolls are also known for automatons. They have Golems throughout Dazaralor, and we encounter some golem bosses in one of the raids (I think BoD, but might be Uldir), the trolls are the biggest stretch for sure though.
But why not Humans?
Humans typically end up using dwarvish technology rather than engineering it themselves, though we do see skyships most human vehicles were created an engineered directly by Gnomes and dwarves. The reason why orcs get Tinker and not Humans is that although the Goblins originally made the Iron Horde technology, Orcs continued engineering it.