The only option I can think of is your organism is already annotated in the databases like STRING, or you can use orthology to assign database annotations (e.g., STRING) to your proteome.

The other options are to use docking tools like HADDOCK or fold-and-dock tools like Alphafold-Multier which both have CPU options, but the runtime for each predicted interaction would likely be measured in hours and days, not minutes. So unless you're only testing a small number of options, your best bet IMO would be to get access to a GPU.

If you're in academia, you can use the Alphafold3 server for small batches, or sometimes you get free access to GPUs on ColabFold, but runtimes are subject to ending abruptly, so I would strongly recommend running smaller batches of proteins at a time.

Cloud providers often offer a small amount of credit when setting up accounts. You could use this to finish a small interaction screen, but it would be a lot of effort to set up.