Hi,
Whilst I can not say for 100%, as I've no experience with sealed-bearing tuffs, it does look like you're correct:
https://www.ebay.co.uk/itm/392278020947?var=0in that, it appears the rebuild kits are just provided with wholy threaded 3/8th diameter axles, suitable 'lock nuts' and a centre sleeve.
So, i'd assume if you have the central sleeve already, and ensure the replacement axle is the right thread pitch for your lock nuts/wheel nuts (24 or 26TPI), then yes, any axle of the right length will do. The rebuild kit mentioned above states a 175mm axle, but I'd imagine you'll get away with anything greater than 150-160mm.
If you've not yet got any lock nuts/wheels nuts yet, then you're more open to sourcing an axle with either thread size, assuming you can also find the same thread size for the lock nuts/wheels nuts, which should be easy enough.
i.e. buy something like this, then remove the supplied cone nuts and spacers, and (if you have it) run the Skyway central internal spacer. All done for ?5
https://www.ebay.co.uk/itm/Bike-Cycle-Bicycle-Cro-Mo-Front-Rear-Axle-3-8-10mm/324053157009?hash=item4b7312c491:g:UpwAAOSwAeBeLCz3you could even then also add a couple of extra lock nuts for safety (good idea) for an extra ?1.75 (once you've confirmed the corresponding thread pitch of the axle kit is the same - email the seller and ask before purchasing):
https://www.ebay.co.uk/itm/BICYCLE-CYCLE-BIKE-3-8-WHEEL-AXLE-BEARING-CONES-15mm-LOCK-NUTS-PAIR-REPAIR/133528400425?hash=item1f16e9b229:g:tDcAAOSwX59fbLOtOthers may come along and provide better advice (we're quite good like that on here
), but this approach should work out ok IMHO.
Good luck.