Hedgies can start eating dry kibble at 5-6 weeks when they start eating pieces the mother has dropped. She should definitely have already been on dry kibble by 4 months--she should have been waaaaaaaaaay before you got her. What did the previous owner(s) feed her? Were they the ones who told you to feed only wet food?
A mix of 2-3 dry cat foods is the best thing to feed her. The wet food should only be considered an occasional treat. Reaper's list that is stickied at the top of this board has all suitable foods on it, so pick 2 or so from there and go with that for your mix.
If she hasn't been introduced to kibble before, introduce one food to her slowly. Put a bowl with the kibble out, and a bowl with a little wet food (not a whole bowl full) and see how she reacts to the kibble. After probably a week of that, if she's eating the kibble leave only the kibble in there and no wet food. Stay with that for a few weeks, with only occasionally treating to wet food if at all, then you can add in a second dry food if you'd like to do so (slowly).
The reason for isolating the foods is to make sure one doesn't cause an upset tummy.
When it comes to wet cat food, I would be reluctant to leave it out during the day due to spoilage. I normally only feed that to my cat, and that is kept in the refrigerator until she's ready to eat it, and it's always eaten in a few hours. I wouldn't leave it out during the day, I think I would leave extra kibble out instead.