A verb "to handmake" seems to be in some use, although it is rare. It would naturally have the past participle "handmade."
I could not find an entry for it in any of the free online dictionaries indexed by OneLook Dictionary Search. However, the Oxford English Dictionary says
trans. To make by hand, as opposed to by machine.
1914 Pop. Mech. Feb. 223/1 The [carriage wheel] spokes were hand-made with a drawing knife.
1971 Ebony Mar. 67/1 (advt.) He handmade the first sour mash Bourbon. We still use our hands in making Old Crow.
2008 C. Cox Vintage Shoes 201/1 All of Choo's shoes were entirely handmade on the premises..—he was handmaking two pairs per day.
Whether or not this is the best wording is a different matter. It would be simple to say instead "made by hand locally" if you prefer the sound of that.
The adjective handmade is older, according to the OED, and much more commonly used than the verb to handmake. In general, compounds of the noun + gerund → noun type, or of the noun + past participle → adjective type, are more productive than compounds consisting of a noun + verb → verb. But it is not all that uncommon for such compound verbs to arise by analogy once there is an established noun or adjective based on the same roots. (Related: What is the etymology of "blameshift"?) Often the use of these compound verbs remains somewhat marginal.