I would say electrolyzer is one of the key machines in any tier.

Problem is, the IV electrolyzer requires osmium which is only available at the end of IV

Since the IV electrolyzer doesn't gate anything by itself, I don't really see any reason why you shouldn't be able to make one when you first enter the tier.

I suggest making the recipe require either 1x signalium wires or 1x tungsten wires instead of 1x osmium wires.

I think the current recipe is fine. At IV you have access to the Tier Four Micro Miner, or if desperate to not craft the first T4 miner manually, you can rush PExC via the alternate route of Platinum Group Sludge Dust for iridium and osmium.

I can agree with this. Manually making a single miner isn't too much to ask for.