How long can a packet of sliced ham be used once opened?
When you buy the sliced meat, take out what you'll use in two days and freeze the rest. If you put wax paper in between portions that you would eat in one serving, or use separate baggies, you only need to pull out what you need. The package might recommend against freezing (for best quality, not safety), but a week or two in the freezer will cause no harm at all.

Personally, I find the 2 day limit a bit extreme, a week should be fine (see luncheon meat on the accepted answer here: How long can I store a food in the pantry, refrigerator, or freezer?). But if you would rather not risk it, the above should work well for you.