As far as I know there isn’t a way to choose where the BigFix client downloads items.
Are you saying that there isn’t even enough space to download a single patch?
You could set the BigFix client’s download cache to be small, which it is by default, and it should download a patch, install it, and then delete it and move on to the next one. As long as these servers have enough space to do at least that, then it should be fine.
Otherwise, it would take a lot of manual effort to mount a network share and install patches from there using BigFix because you would have to place the items into the network share yourself and write the code to install them yourself if and only if they are needed, or you would have to re-write the fixlets provided by IBM to use the network share.