Eenteresting... I've never heard of silk liners, but it makes an awful lot of sense! My guess is that you would not want raw silk, you would want a nice smooth silk. Reason being, you want something as smooth as possible, no abrasion at all. Raw silk is wonderfully soft, but not very smooth at all. I would also recommend getting undyed silk - truely natural colored would be perfect, but you'd probably have to special order that. White would be fine. I find that dyes from silks bleed horribly and you don't want a green baby bottom... not to mention the fact that the chemicals would probably irritate baby more.
As for cutting and handling it, it's not tough. It's a bit more slippery and frays slightly more than cotton, but I don't think you'll find it very difficult to work with. Personally, again on the non-abrasion thing, I wouldn't serge the edges. I would give them a narrow folded or rolled hem with a regular machine.
However, I think the *only* effective way to treat diaper rash is to leave baby undiapered as much as possible. Lay your daughter down to nap or play on top of some towels or a changing table pad. If you're home during the day, you should be able to arrange things so she's diaperless all day and only worry about diapers (and silk liners, etc.) at night or when you go out.