It's certainly paradoxical to say that a 'he' is a 'sine qua non', since 'qua' is feminine, and 'he' obviously masculine. The original phrase refers to a feminine noun: 'condicio sine qua non...', 'the condition without which...', a phrase which became such a cliche that it could be understood even with the 'condicio' missed out. Trouble is, once you say 'he is my sine qua non', you have filled in the gap with something else which has the wrong gender, and it kills the grammar of the thing.
You can fix the grammar with 'ille mihi est sine quo non...', but then it stops being a cliche, and you need to be explicit about what goes in the gaps: 'he is for me the one without whom...<what?>'. But of course, the rest of your sentence just repeats it. "He is for me the one without whom <...>, without him I am nothing."
You could fill in the missing 'condicio': ille mihi est condicio sine qua non... = he is for me the condition without which <what?>. But you're still repeating yourself a bit in the second half; and I'm still wondering what happens in the gap: without which what happens?
I hope some of that made sense. Basically I'm agreeing with Matthaeus that the best solution is to compress it into a single phrase.