General aviation pilot reported runway excursion during landing. Pilot taxiied back onto runway and then to parking.

Narrative

I was landing on Runway 23 shortened using the RNAV 23 Z approach in IFR weather with mist/light rain falling. I saw the Runway environment just as we hit minimums. I was high when crossing the threshold; leading to a landing approximately 2000-2500 feet from the start of the Runway. The Runway was shortened from approx 6000 feet to approximately 5000 ft due to milling and repaving work in the first 1000 feet of the Runway 5 approach end. Upon landing and applying the brakes; the aircraft began to shimmy back and forth; apparently sliding on the wet surface. I let up on the brakes in order to regain full directional control and then gently reapplied the brakes. Ultimately I inadvertently continued into the work area; a recently milled asphalt surface; at the end of Runway 23 before being able to completely stop the aircraft. Tower notified me of the overrun into the work area and had me back taxi on the Runway to taxiway echo and instructed me to taxi to my intended parking. There was no apparent damage to the aircraft. In retrospect; I should have executed a missed approach and re-attempted the landing.