Since the finish I'm using is water based, is using steel wool in this process okay?
It's not ideal but you can use it if needed.
But I would recommend not using it lubricated with soapy water as the potential for rusting is very high — I've put pads down I was using to clean glass and just a few minutes later have come back to them to find the pad sitting in a small puddle of rusty water.
If it's not ok, what are some alternatives?
An incomplete list includes:
- finer abrasive papers/films or sponge-backed abrasives
- bronze wool
- stainless steel wool
- powdered pumice and/or rottenstone powder
- non-woven nylon abrasives AKA synthetic steel wool
- automotive scratch removers, rubbing compounds and polishes
This shouldn't be read as a list of alternatives only as various combinations can be used in sequence, e.g. abrasive papers up to a high grit number, then rottenstone lubricated with a light oil, finally using a fine automotive polish or swirl remover.
I've seen synthetic steel wool, but the ones available at the local big box stores seem to be of not very good quality.
It is wise to avoid this if the quality is suspect, because the abrasive grains tend not to be graded well in cheap stuff. This can lead to scratches just like you get if an abrasive paper is contaminated by a speck of grit from a coarser grade.
Note: do be sure to wait sufficient time before starting to ensure best results. While the short drying time of waterbased finishes seems to indicate a very fast cure time it's still generally necessary to wait at least 48 hours, sometimes as much as a week, for the finish to harden completely.