We would strongly encourage warriors to treat combat blunt axes as though they were sharp ones, and consider making a leather cover for the axehead. Would you really feel comfortable having a sharp hand axe in your belt (especially if you trip over...)?
Wooden axe covers
A small number of wooden axe covers have been found in Hedeby, Schleswig, Dublin and Novgorod. These are discussed in a useful article by Tomáš Vlasatý. Comparing the size of the covers to the typology of medieval axes suggests that they date from the 10th to 12th centuries.
Making a wooden axe cover
Axe covers seem to have been made by carving a groove for the axe blade into a piece of wood: willow is the most common (4 of the 18 known examples), though yew, oak, ash, spruce and birch have also been found.
Cord or leather thonging was then used to tie the cover in place, either with two holes (at top and bottom of the cover) or with a hole in the middle of the cover.
Leather axe sheaths
A highly decorated leather axe sheath was found in 14th century Novgorod. While this example comes from some way out of our period, the strong links between Scandinavia and Russia make it worth noting; it is possible that similar examples will be found in western Europe.
Making a leather axe sheath
Take one or two pieces of leather of a size that could cover the blade of your axe. You can either fold one piece in half or stitch two together, which may be easier. You need the 'sheath' bit to cover the axe blade (furthest away). The simplest thing may be to cut two bits of leather, each at least a cm larger than the axehead. Sew them together on the blade side and the bottom.
Hey presto, you can slide the axe shaft in and then drop the head/blade into the sheath where it will stay securely. You have the option of a bit of leather thonging to tie the sheath closed for travel (to make it look really authentic). The (sharp) blade will eventually cut through the stitching, but that's better than doing yourself an injury.
Then decorate the flat sides of the axe sheath. <gallery mode="nolines" widths=500px heights=500px perrow=7> File:Axe sheath 4.jpg|Example of a leather axe sheath, courtesy of John Gendall <\gallery>