I have the same record and the same "problem", though I don't consider it that problematic. Your dealer is correct, the hiss will be probably be markedly reduced through use of a mono setup. I agree with Eldartford, though, there are a lot of records of that vintage with hiss and they are still enjoyable. I think the key word in your post is "constant" hiss. No record cleaner will remove that, it is part of the recording.
Mono vs Stereo LP's
I recently purchased a 1958 mono issue of Art Farmer's "Farmer's Market" on the New Jazz purple label (New Jazz was a Prestige specialty label) The record looks to be in near mint condition and was carefully cleaned by me with a record vac. The recording, however, plays with a constant background noise or hiss. The dealer who sold me the record has a reputable history and is telling me the noise is because I need to play the record with a mono cartridge rather than my stereo Shelter 501. I have read the threads on Audiogon regarding mono cartridges which say they can sound better, but don't suggest there would be the type on noise I am hearing with stereo. I have many other mono records of similar vintage and have never encountered this before. Anyone have a similar experience to this?