I'm right handed and right eyed but have a dodgy right eye so shoot left handed.
It felt really uncomfortable to start with but I've got used to it now, at least the shooting part, it still feels really awkward to even sit down for a left handed shot.
Air Arms S410F .177, AGS 4-16x50, AAF 4.52
Air Arms S400 MPR FT .177, MTC Viper 4-16x50, AAF 4.52, Cloverleaf service
BSA R10 .177, MTC Viper 10x44, JSB Exact 4.53, MWSS200 moderator, UKNeil adjustable cheek riser