Depends on the forks and how much oil is coming out but for a small amount sometimes you can put a bit of rag or sponge or something between the dust cover and the seal to soak up a bit of oil that would otherwise dribble down onto the tyre. Just check it / change it every fuel stop / night stop.

I have memories of topping up leaking forks with 20-50 engine oil and wishing I hadn't the first time I went over a pothole as the forks were essentially solid. I may well have put too much in but it got emptied out very quickly as riding around leaking forks was preferable to double vision and loose fillings. :(

Well, I got the forks fixed! Thanks all for your feedback and tips.

It takes very little oil to make a big mess.

If you must use something for the fork oil ....
ATF - Automatic Transmission Fluid ... is about 5w .. and that should be ok for fork oil replacement untill you can get the good stuff. It is certainly better than 20-50w! To gauge how much to put in ... well the non leaking side will give you the height of oil in the leg that is required. A bit of wire to act as a dip stick and you have a good idea of where to have the oil in the leaking side.

I think ATF is 10W. At least most of them. If your manual is stating 10W, you are good to go for ATF.

Still better than 20-50w engine oil...
Personally ...
I'd not be topping up the fork oil untill it runs towards dry or repairs are completed.
I'd put a rag around the fork leg to try and catch the oil before it makes a mess or gets on the brake. Remove the rag at the end of the days ride and squeeze out as much oil as you can.. bet it won't be much.