I have a pair of ltm 2800 load balancers in a failover pair, active/standby.
I want to upgrade from 126.96.36.199 to 188.8.131.52, will I be able to to the standby device, then fail over to it with minimal disruption?
Can I also go from 184.108.40.206 to 220.127.116.11 with no issues?
Yes you can (you can't directly go 16 but you can go directly to 15.1.x):
Also your device is i2800 as I don't know just 2800? Check if the platform supports 15.1.x as I see if it is i2800 it should support it.
I suggest to check this extra article:
And if you have GTM/DNS there are special considerations:
About if you will have issues or no one can tell you that 100% there will be no issues but if you follow all steps 90% of the time there will be no issues. If for some reason the config does not load after the upgrade use "load sys config verify" before reverting to 13.1 and try fixing any error messages (ignore the warnings) and check google or the f5 bug tracker for the error (https://support.f5.com/csp/bug-tracker?sf189923893=1).