Not (being) good at swimming, he didn't like it.
There is no problem omitting being in such phrases.
Other examples include
[Being] afraid of water, he didn't like swimming.
Not [being] good at swimming, he became a boxer.
See also 12 other example sentences (Numbers 12-23) in a similar question and answer at Azar Grammar Exchange. The first post is the question, and the second post gives the answers to each numbered sentence.