FD capacity numbers tend to be conservative, although I have no experience to say if a FD rated with 22t capacity would handle 26t or 28t diff between small and large chainrings.
If you have bar-end shifters (so, non-indexed front shifting) you could put on FD with higher capacity.
But that would already be getting into territory where you'd be spending as much as just buying a cassette with 11t small cog.
I'd say, mount your FD as high as you can (that will still not bump the chain in the small chainring) and see how much space you have above the large chainring teeth. This will give you a sense of whether you could update to 48t or 50t large ring.
If not, just get a new cassette with 11t cog.
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"c" is not a unit that measures tire width