In I Love Lucy Season 1, Episode 23, The Mustache, Ricky uses an electric shaver to remove the mustache. The logo on the shaver can be seen in the screen capture above and it looks like a good match for Schick 20 Electric Razor pictured below,which is a working model currently for sale on eBay.

The Schick 20 was widely advertised in 1952 the year this episode was made.
See all Schick 20 Shavers on eBay
Incidentally, Ricky is shaving while looking into the Bacchus Mirror we identified in a previous post.

The Industrial Designers Institute (IDI) a predecessor to IDSA, initiated the first national design awards in 1951. One of the first product designs chosen for an award was the Schick 20 designed by Carl Otto in collaboration with Norman Gray, the chief engineer at Schick. The Schick “20” had redesigned internal components for a wider, shorter form, making it easier to grip and use than the previous long thin shavers that were standard . The golf-ball-like dimples on the surface also improved grip. This new configuration set  the precedent for future shaver design.
Ref: http://www.industrialdesignhistory.com/node/186

Note:  The Custom Schick Super Honed shaver in a dark brown case looks very similar to the Schick 20, except the top section was all metal however this model was not advertised until 1954.  A search for Schick Super Honed on eBay will sometimes bring up a few misidentified earlier Schick 20 models,