If the claim is that it was made and sold by Paul Fischer then it’s obviously a mistake. I’ve seen numerous documents bearing Paul Fischer’s signature (correspondence, draft registration, Social Security application, etc), even visited his grave, and every single time it’s spelled Fischer. Similarly all other firsthand records (eg from the State Department archives) or records from people who knew him (employers, his wife, etc) spelled it Fischer. If it’s occasionally spelled Fisher by a third party (a reporter, census taker, a book author, etc) out of ignorance or sloth that carries no weight. If you’re not German it’s an easy mistake to make but it’s still a mistake.
So if the question is “is there more than one correct way to spell Paul Fischer’s surname?” or “did he ever spell his last name Fisher?” the answer is no.
Fischer was a highly trained craftsman; he was not illiterate. He knew how to spell his own name and consistently did so the same way throughout his life.
Incidentally this is what Fischer looked like when he immigrated to America just before the outbreak of WW2:
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As for the leather wrapped pipes I have no idea if Fischer produced them or not. It seems unlikely for several reasons but in any case Fischer was a meerschaum carver not a leatherworker and the covers would have been made by someone else. I will say in passing that I’ve never seen the nomenclature on the stem of your pipes on a bona fide Paul Fischer, or for that matter a black stem instead of a yellow one, but of course “never seen” and “don’t exist” aren’t synonymous.
As an aside, if it’s not a mistake on the leatherworker’s part as an alternative source there were a few Fisher Pipe Shops floating around over the years; maybe one in California and one in Ohio?