Is Part 91 Instrument currency for SIC similar to Part 135 requirements?
Only if you fall under the Fractional rules (Subpart K).  Otherwise SIC currency requirements for turbojet airplanes are specified in 14 CFR 91.531, which requires you to be current via 14 CFR 61.55 and has no instrument currency requirement (although you do need your instrument rating to fly under IFR).