One possibility (admittedly, and ugly one, but...) is to extract the individual object files from the static library. If the function you're calling and the function it's calling are in separate object files, you can link against the object file containing the function you need to call, but not against the one containing the function it calls.
This only gives you granularity on the level of complete object files though, so if the two functions involved are both in the same object file, it won't work. If you really need to get things to work, and don't mind making a really minor modification to the object file in question, you may be able to use a binary editor to mark the second function as a weak external, which means it'll be used in the absence of any other external with the same name, but if another is provided, that will be used instead.
Whether that latter qualifies as "modifying the library" or not depends a bit on your viewpoint. It's not modifying the code in the library, but is modifying a bit of the object file wrapper around that code. My guess is that you'd rather not do it, but it may still be the cleanest way out of an otherwise untenable situation.
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