For most cases, the addition of 6X his tag should not lead to a significant decrease in the specific enzyme activity, since 6X his tag is a very mild small tag. If that does happen, usually what you just need to do is switching the 6X his tag to the other terminus (i.e., if N-terminus 6X his tag does cause the problem, then use C-terminus 6X his tag).

It shouldn't but it could, depending on how far the attached terminus is away from the active site. My tagged membrane protein has lower specific activity, but the tag I used is longer than 6xHis. You may want to consider adding TEV recognition site between your protein and tags.

I work with a membrane protein that carry a C-terminal 6x-His tag and there is no decrease in its specific activity. However if your protein has cloning artifacts (extra residues) besides the 6x-His tag, then it might hinder the activity.