Actually before you even do that I'd look at the cleanser they're using. Clean skin will moisturise better than flesh with soapy residue on it; Dove has a nice little package available this year of gentle cleanser plus Hydrate+ moisturiser which have the benefit of being completely unscented. They do the job as well as some of the vastly more expensive alternatives you can buy.
Likewise Rehab London (pictured) offers a couple of different moisturisers that won't add their own scent, which is always welcome. Morning Glory is aimed at normal skin, if you produce a little more oil than the rest of us then fine, they have a "no Shine" option (pictured) which works very well indeed. And yes moisturiser is still a good idea after you've shaved even if you have oily skin because it will soothe you - you've just dragged a naked razor over your skin, remember? (And don't forget to use a decent shaving cream as I've recommended here).
If you want something for your whole body or just a few chafy bits (spare us the details) then you could do distinctly worse than Palmers' Cocoa butter formula body lotion, which I've been trying out and is very pleasant stuff. Its only drawback is that you do end up niffing rather of, well, cocoa butter, which isn't at all nasty but will clash with any cologne you might want to use. I put some on after trying out the Original Source Orange and Cinnamon shower gel that's out for Christmas (rather cleverly the company gets its customers to vote for which gel should be released during which season) and ended up smelling like a chocolate orange. Each product is fine by itself but watch those combinations!