Not every bidet needs one since the water comes in pressured. This is the one that I got that does not. American Standard 5900A05G.020 Aqua Wash Non-Electric Bidet Seat for Elongated Toilets, 14.9 in Wide x 3.6 in Tall x 21.1 in Deep, White - - Amazon.com
No problem. Good luck! I had specifically had this one for a couple years and really liked it.
If you can afford a little more and have a gfci outlet in the vicinity you could also just make the jump to an electric seat. I recently got the bio bidet a8 and now I can’t imagine going back to a non electric. It is on sale at costco for 250$ right now and the extra 150$ gets you a lot of features and would also solve your problem.
I self installed this one. It came with everything necessary to self install so I did not have to run the the hardware store (something to consider when buying).