This question sounds like you are trying to provide a help desk for your users when they create issues. For which of course the answer is JIRA Service Desk.
However, as your question is tagged with JIRA-core we also need to consider how you could achieve your modest requirements without the overhead of JIRA Service Desk. To do this you will need to change the behaviour of the screens - as you are aware the layout and content of screens is defined by the standard and custom fields that you add to the screen, there are no options within the UI to change the way in which these are presented. So that leaves edit the underpinning code that works for all screens in your JIRA instance. - But this then adds more challenges for future upgrades as you may have to repeat or even rework your changes.
Can anyone else suggest an alternative approach?
I'd modify the footer to add the help links, rather than a button. As you say, it's code change, but it is minor and well documented.
The other option is to use a message field in the JIRA toolkit - that would let you inject some text and a link into the field area without needing any code.
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