There is a Fry's up the street so parts are readily available.
Never been to a Fry's but I understand it's an experience...
Anyway, the circuit you found is intended for a guitar pickup. Should be no problem but I would add a DC blocking cap to the input, something like a nice 16 volt mylar in the .22 to .47 range. Same deal on the output. C1 is intended to ensure the output is clean audio with no DC component. 4.7 uf is too heavy IMHO and an electrolytic is polarized which is a no-no to an audio purist. A .47 mylar should work mo'better since a clean midrange is all you care about on the radio. C2 is intended to stabilize the battery voltage during peaks, especially when the battery is near flat and could use a little reserve charge from an electrolytic. 100 uf is a good value. Make R4 a 50k trimpot and connect the wiper arm through a .22 uf mylar to the mic input of the radio. Make it somewhat accessible since that's the adjustment for output level.
As for the Shure 444, that is my favorite desk mic and I adapted a Lo-Z version to an Icom IC-756 that came stock with a phantom powered electret hand mic. Used a slightly revised version of the Shure schematic I linked for you. Works FB, no outboard box, built into the base of the mic and is phantom powered by the radio. Almost looks like I planned it that way. If you decide to try that circuit the transistor is a generic NPN like a 2N2222 or 2N3904 and it's very un-fussy.
Finally, 'NYY is correct in that if you can find an original Hi-Z 444 (grey case) all you need do is wire a connector. That's exactly the type of mic the radio was designed for. If you end up with a Lo-Z 444 you will need a pre-amp otherwise the mic will be a real scream to work with..............