I'm far from any kind of expert but in the last 2 weeks I've restored 4 axes so my little bit of knowledge may help. For removing the rust and/or patina a good overnight soak in Vinegar works wonders and no heavy wire brush needed. A good scrub following the soak with a rag (you will ruin it btw) and then a modest hand sanding with 120 or 180 grit.
If you need a new handle call House Handle and speak with Megan. She was great with helping me get the correct handles for the 4 different axes I was working on. Their number is Remember to try and have the dimensions of the "hole" where the new handle (haft) will be inserted. Also, make sure whatever handle you order comes with both a wood and an aluminum shim.
Pick up some boiled Linseed Oil to either refurbish the existing handle (after sanding down to bare course) OR to finish the new handle you have ordered. Btw, if you go the new handle route do your husband a favor...order the new haft with NO finish applied...it's an option that House Handle will do for you. Any varnish or poly is abrasive to the skin even with moderate use. You really want nothing but Linseed Oil to be applied...preferably in multiple coats with a light sanding (220 grit for me but it's personal preference) in between.
Lastly, if it were me. I'd put together the pieces of the puzzle but I would only strip the old axe head (vinegar mentioned above with a good wipe down) and coat with some linseed oil (keep the rust from coming back while you wait to give it to him). Put the handle, axe head, sandpaper, oil, (a nice pair of work gloves, hint, hint) and let him do the rest of the work. He'll likely enjoy it more if he made it his own.
My .02 Have a great B-Day PARTY!