Fear not, fellow shaver; Mr Harry F Partridge patented the solution back in '46 - the aptly named "appliance for vibrating a safety razor". Sleek and unobtrusive... uhm.. well, lumpy and rather obtrusive to be honest... anyhow... you simply clip the appliance onto your razor - or rather; you clip your razor into the appliance - and said appliance improves the shave in much the same way painting go-faster-stripes on an old POS car turns it into a sleek, modern race car. In other words, probably not at all.
In Mr Partridge's own words:
My present invention relates to an improved razor and more particularly to a means for mounting and reciprocating the conventional safety razor wherein the razor including its blade is reciprocated in short swift strokes longitudinally of the blade and the blade head so that the razor will vibrate laterally as it is drawn over the face of the user.
I'm more or less at a loss for words here -but then I'm of the firm opinion that the only thing a vibrating razor is good for is reliving the user of more money compared to a non-vibrating razor.
Mr Partridge again:
This vibration of the razor head and its blade will increase the cutting effect of the razor blade and will result in a vastly improved shaving operation with a closer shave and a less painful shave.
I'm sorry to break it to you, but if your shaves are painful you're quite simply doing it wrong. Try with better prep and a sharp blade - I can all but guarantee* you a smoother, closer and painless shave.
*) Not a legally binding guarantee, Offer void where prohibited by law. May be too intense for some viewers. If condition persists, consult your physician.