I just got one myself.
Remember,first thing to do is remove the set screw from the head/haft.
IMHO about the only thing I can see the Pipe Hawk needs is the cutting edge refined and lightly deburr the edges of the eye with a file to ease assembly/disassembly without gouging the haft in the process.Head to haft fit on mine is real tight,so no need to do much there.
Otherwise,the Pipe Hawk is the most well rounded design hawk Ive had to date,and so far is showing to be a exceptionally functional field tool.
Personally,Im just going to use the hawk as it came.Once the finish on the head and haft wears with use I will refinish by stripping the paint from the head and cold bluing.The haft I will eventually add some carvings for grip enhancement and decoration,lightly sand and refinish with a few coats of Birchwood Casey Tru-oil for a hard finish and seal the wood.
I would not sharpen the back of the beard.Ive done that on previous hawks and it basically places a sharp edge to your hand and gear.I prefer the back of the bits beard to just be functional as a hook and not a cutting edge.
The hammer pole is about the perfect size without affecting the balance of the bit,so I'd leave it as it comes,especially if this is to used as a tool for field use.