Can I reclass after getting to my unit?

Go USAR and request to reclassify. So long as there is a position and the Cdr says yes, you go.

There are two routes to reclass to a new MOS in the Guard, they are both the same, the fist step is just reversed.
1. You request an Exception to Policy (ETP) on a 4187 to attend the new MOS school, explaining when the course is and where the new duty position for that MOS is that you will transfer to. If approved, you attend that course and transfer to that new position.
2. You request an ETP transfer non-Duty MOS qualified (NDMOSQ) on a 4187, explaining when you are reserved for the new MOS school, and where you are transferring. If approved, you transfer to the new job, then attend the MOS school.
Either way, your first assignment requires two years of stabilization prior to any transfer. To shorten that two year period will require another ETP.
The approval for these specific ETPs is the G1 of your state.

Another option would have be to just contract for the MOS you want coming into the Guard. If there is a vacancy for that, this would be the easiest route.

Typically they make you do at least a year in your current mos.