There is no correct spelling of your surname.
Sure, there is now. It's Wasmanski. Unless one of your modern-day relatives spell it differently, and they might.
It is possible your current spelling is a change from another established spelling.
It is possible the other spelling is a mistake (also be sure you're looking at the original document and not a transcription).
But it's most likely that there were variant spellings.
People just didn't care about spelling in the past like we do today (at least officially). You got all sorts of versions of a name and, yes, some may have a slightly different pronunciation.
Then there is the issue of different alphabets. If you're converting to English from a non-Roman alphabet (like Cyrillic), different spellings are meaningless; they're just transliteration variants.
But even if you're going from one Roman alphabet to another, there are different letters and also markers on letters. It's not always so straightforward to translate these. Just to make it even more complex, the country and language changed multiple times. German and Hungarian don't pronounce letters the same and they have different markers, for example.
Don't think of it as something you have to know before you can go further. Just assume there will be variations and roll with it. Record every one and cite the source. And keep on searching.