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Idea is OK, but..
Beam splitters are "lossy".. that means they attenuate light by at least 1/2, but normally much more that that. So you will have darker images in both camera and viewer.
I think the better idea is flip mirror.
Get a cheap, film, mechanical SLR from ebay and mount the webcam sensor in focal plane. this way you will have maximum light transmission in both optical paths, but not at the same time, of course.
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