There is a good chance that the shower curb (and maybe the whole shower) was not constructed properly and there could be a lot of rot in there. The curb should have a waterproof liner applied over the top and down the outside of the curb. then, metal lath covered with mortar. That could then be finished any way you wanted to on the outside, but the top and inside would normally be tiled (as the outside typically would). So, without some additional idea of what you really have, might only cover up a disaster waiting to be discovered. If you take an ice pick and push it into the wood of the curb from the outside, is it solid or all punky? If it is soft and rotten, it may be time to tear out and redo.
Check out www.johnbridge.com for further help with your shower.