Upgrade to 11.6.1 from 11.6.0 HF6

11.6.1 and 11.6.0 both have the same license check date, so you won't actually need to re-activate the license before upgrading, but there's no harm in doing so, other than a slight risk, which is that because re-licensing causes your config to be reloaded, if you've been making changes in tmsh, and not saved them, those changed would be lost. Any changes made in the GUI are automatically saved immediately.

Whilst I personally have't seen any significant issues encountered during a minor upgrade of 11.6.0 HF6 to 11.6.1, it doesn't mean that none are possible. Because everyone's configurations are different, it's impossible to say with 100% certainty that nothing will go wrong, so the best approach is to ensure you perform comprehensive testing. A side effect of doing this is that you also ensure you have complete and current documentation of all the services that your BigIP provides.

In the event that something does go downhill, you can always generate a qkview, boot back into the previous boot location, and then upload the qkview to ihealth for analysis.

It's also worth reading the release notes for ASM, APM, and LTM/TMOS, to see if there are any changes or known issues with features that you are using.