As I recall, all the lotions, etc. are kept in the bottles/tubes. Only the mud is in three bowls with no lids, and I think as long as you don't use the mud (which, if I remember correctly, had a scent to it that probably would be stronger in the steam), your DH should be fine. The steam room is a different room, and as long as you don't put the stuff in there, it shouldn't be too bad.
The creams in the tubes/bottles are all in a basket in the middle room, and you can sample them to see if they are mild enough for DH. To be sure, if you want you could bring in something of your own, stick it in the pocket of your bathrobe, and that way you'll have a back up if the stuff there is too strong.