You can try it, but you may discover a loss of accuracy. I am right-handed, but left-eye dominant. When growing up, I shot a rifle left-handed and a handgun right-handed. I got through an Army career and a lively combat tour shooting that way. I qualified expert consistently with a .38 Special snubnose, a .45 ACP 1911, M-14, and M-16. Nobody ever mentioned eye dominance or questioned the way I shot a rifle. That continued until I went through a tactical course after I retired from the Army and joined a Defense Department agency. The first item of business for the instructor was to determine eye dominance of the students. After we discovered I was left-eye dominant, he insisted I switch primary hand from right to left. I protested, but he offered to let me go back to using my right hand as my "strong" or primary hand if I didn't see an improvement in accuracy and little or no loss of speed in drawing my handgun or follow-up shots. Let me tell you, I was terrified at the thought of going through drills where I had to clear my clothing, draw, fire, clear a malfunction with my left left hand only and my left heel or fire between my legs while on my back. We took each drill very slowly until some muscle memory set in. At the end of the day, I was noticeably more accurate and my speed was acceptable. I practiced red gun drills a lot! That was years ago. I shoot a handgun left-handed now. All my leather is for a lefty. I didn't lose anything with my right hand. When I purchased a SIG GSR 1911, I added a Wilson ambi thumb safety. Now...reloading a revolver is a bit tricky. I have to switch hands when I reload, but I still shoot primarily with my left hand.
So, that's my story. Funny, I also own a P226 in 357 SIG. I shoot it with my left hand without a problem. Is it the expended brass that bothers you?