I think it's a great idea to make up a list of all the variant spellings that you find for anyone in your research -- including mistakes that happen because of weird indexing and bad OCR.
When we are searching online, we aren't looking directly for the records -- we are searching computer-readable pointers to the records.
Tools for better searching
For searching passenger lists, the gold standard is Stephen P. Morse's One-Step Webpages. Some of the forms offer options to search without the surname at all, or to choose between "starts with or is", "sounds like", or "is phonetically". The latter option has a label which is a link -- click through and you'll find the page Beider-Morse Phonetic Matching (BMPM) which has the source code for developers. The three links at the bottom that page -- the table of tokens, and the two articles on better Soundex, are papers where Beider and Morse explain how it all works.
This paragraph shows which websites have implemented Beider and Morse's improved phonetic matching:
There currently exist several implementations of Phonetic Matching. It is on several databases on my website (http://stevemorse.org) -- namely the Ellis Island database, the Dachau Concentration Camp Records, a database of Jewish surnames, and various naturalization databases. Other websites that have implemented Phonetic Matching are http://sephardicgen.com, http://jewishgen.org, http://jri-poland.org, and http://rtrfoundation.org. In addition, there are several other sites that are currently considering adding Phonetic Matching to their search applications.
Make your own phonetic chart
James Beidler (not to be confused with Alexander Beider cited above) makes up a worksheet when searching for German surnames with all the possible consonant variations and wildcards for vowels. Check genealogy guides for searching for Polish families to see if other researchers have used the same methods. Keep an eye out for software, too -- I once found a wonderful little surname generator (for German surnames) that would make up the kind of list you're looking for.
Misspelled OCR
You may come across a printed index of passenger names that has been converted to computer-readable form via the process of OCR (Optical Character Recognition). Kenneth Marks of the site The Ancestor Hunt has a series of articles that are a tutorial on how to get around bad OCR when searching old newspapers, and a tipsheet showing letter pairs that are often confused.
Hunt's site is well worth exploring if you can't find passenger lists -- very often you can find clues to arrivals of other family members by searching in the social pages of the newspapers, or can narrow down the date of someone's arrival in the US from clues in their obituary.
The set of letter pairs that can be confused in handwritten passenger manifests will be different -- you might be able to find a similar table in articles on reading old handwriting. If I can find a table, I'll link it in here.
Resources and Further Reading