A Center Controller reported they issued a heading to an aircraft that placed it below the Minimum Vectoring Altitude.

Narrative

ZZZ was landing RWY XX/XY. We don't work this configuration often. Usually only during this time of year and for only a few days. Aircraft X was cleared for the RNAV XX behind Aircraft Y also cleared for the RNAV 20. After I switched Aircraft X to ZZZ tower; tower called me and asked if Aircraft X had the preceding aircraft in sight for wake. I told them he didn't say anything to me and that I had just switched them to tower frequency.Shortly after; tower called again and told me Aircraft X was on the missed approach for wake turbulence. When the pilot called; I instructed them to maintain 040 and fly heading 075. Meanwhile; I was managing other arrivals. As I was clearing another aircraft for an approach; I noticed Aircraft X approaching a 063 MVA. When the pilot finished their readback; I instructed Aircraft X to fly heading 360. The aircraft began entering the higher MVA so I instructed an immediate 360 heading.We are a combined facility with tower/approach and center controllers working in the same building. For some reason; center controllers work ZZZ approach. This is the only approach environment that we work. All other sectors are enroute rules. We are in the process of giving the tower/approach controllers ZZZ approach. This process has taken a very long time. As more tower/approach controllers certify; the enroute controllers work ZZZ approach less and only fill in when staffing is needed on the their side; which is causing us to be less proficient/efficient. The transfer of ZZZ needs to be completed.