If all clients are running Java 7 update 51, you can update Ignition to v7.5.11 with no problems … except for the Mobile Module. The Mobile Module requires Java 7 on the server. It’s not the same as updating to v7.6.x, but it is something that resolves the security problems.
In this thread ( viewtopic.php?f=70&t=11216&p=40096&hilit=applet#p40096 ) Greg Simpson say it’ll be fixed for 7.6.4 but didn’t say nothing about 7.5.11. I’ve also checked the changelog of 7.5.11 but there’s nothing specific about that.
I don’t use the mobile module of ignition, so it’s a starting point anyway, but it would be nice if any moderator confirm your advice!
We have already done the upgrade numerous times, but why not try it for yourself? Download an older version (7.5.6, for example) and install it locally and test the site localhost:8088 with Java 7 update 51 installed, then upgrade to 7.5.11 and try it again.