I'm a big advocate of the hand washing in the sink. That said, I also own an Uhlmann with the washable removable padding. Luckily, unlike the Triplette bib liners that have the velco part that adheres to EVERYTHING on the bib, its in the mask with the Uhlmann mask. So you can wash the liner with other things and it wont snag.
I did this, though, and I'll warn you it may shrink.

Not too badly, but right before a major two day event I threw both my liners in the wash on cold, and then suddenly neither fit in the mask the way they used to. I was so distraced thinking "my mask doesn't fit right!!!" that I wasn't paying as much attention to what SHE was doing on the strip. Ooops.