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.
The only questionable thing about your sentence is the use of it. We can't be sure whether it refers to
1 swimming
or to the whole phrase
2 Not (being) good at swimming
Most native speakers would probably interpret it to refer to swimming.
But it is possible for a pronoun to refer back to the entire -ing phrase. Here's one example:
Although [being] a poor swimmer, he didn't let it bother him.
It refers to the whole phrase [being] a poor swimmer.