Don't quote me on this as i'm just speculating and don't know from experience, but I think that if you simply delete the .txt files, I believe they will just be recreated as needed. Even if you don't come into any threats that need to be blocked, the Shield reports are edited and updated each time you restart your computer with "shield stopped" and then "shield started" as the shields obviously turn off and on when you power your computer of and on respectively. So even if you delete the .txt files they'll recreate.
You can, much more safely, also disable the reports being created, or at least updated, in the first place in Avast's settings. Go to the settings, Protection, Core shields, and for each shield Untick "Generate report file". That will at least stop further information from being added to it.