Is declining an undergraduate award which causes me discomfort appropriate?
I suggest a third way:

Write a concise e-mail to whoever is handing out the award that you would prefer to receive it silently for the reasons you cited (not wanting to be reminded of your disease), i.e., without being mentioned at the ceremony, but via mail or similar.

This has several advantages:


You spend at most as much energy on this as declining the award, probably less since you do not have to worry about how to politely decline it, etc.
You avoid what you want to avoid.
You will never face regret for not taking the award and in the future you are completely free to use it or not (for your CV and similar).