Whether or not your query processing instances have administration access will depend on how things are configured.
Technically each Funnelback server has an administration interface but on query processing machines these are often disabled or blocked.
Funnelback servers can also be put into the prepare for upgrade mode via the administration API - if you log in to the query processor you should be able to trigger this via the command line.
Once the server is prepared for upgrade you should be able to run the installer in the same way as on the administration server.
I'm not sure how you normally upgrade but we often recommend that you clone your existing VMs and upgrade the clones, then cut across to the upgraded version once you're happy with it. This enables you to upgrade and deal with any issues without affecting your currently live search, although it is possible to achieve a similar result in multi-server environments if you upgrade things carefully.