Don't use a bench grinder you will over heat the edge.
Most of these do not have a heavily hardened edge. You can get by for touch ups with a circular stone generally; for redefining the profile when its been improperly sharpened at too blunt an angle you can generally use a file to get that done.
One of the exceptions to the reasonably soft steel used are the "hewing hatchets". They have (or used to have, no clue how they make them these days...) an inlaid hardened steel section on the flat side, and those are tougher to resharpen properly. the main head is soft enough to file, but the hardened steel insert is not. (The also have/had a hardened steel inserts on the "hammer" face, and this is so brittle I see them chipped sometimes)