Both Trumpeter and Italeri make an LCM(3) in 1/35 scale. The hull on the Trumpeter kit is a little deeper, so there may be a little more room for RC parts.
I converted the Trumpeter kit to RC a couple of years ago. Here's a link to a picture on our club website:
http://www.marinemodelers.org/gallery/military/LCM.jpegI used two standard servos for the power plant, connected to a Y cable, so I could use a cheap 2 channel radio. I build my plastic RC conversions as sealed models, so I used a 2.1 Ah NiMh battery, and just built it into the hull under the well deck. I figure that by the time it wears out, the model will be as worn out as well. The cargo well deck is sealed, so it doesn't matter if any water gets into it.
Note that the LCM(3) was not used to carry Sherman tanks-- it was found that the tanks were a little too heavy for the boat. The LCM ws designed to carry a 30 ton tank, which was about the weight of early Shermans, but by 1944 the tanks were pushing 40 tons. (The LCM(6) was an LCM3 with an additional 6 feet of length amidships, which increased the boat's displacement enough to let it carry Shermans.) The LCM3s used at Dday would have been carrying troops or lighter vehicles, such as a halftrack, truck, etc.
I used a Sherman in mine because I found a nice diecast motorized model, I was thinking about launching it via RC at some point....