A straight razor works pretty well, but the blade will wear pretty quick from sharpening. It is so thin that sharpening eats it away. The good news is they are cheap.
As much as I hate to see good shaving irons used this way, and well know the frailty of those blades-as I've only shaved with refreshed vintage straight razors for several years now, I'll weigh in here on the use of SR's for patch knives from the modern perspective of practicality and preservation of useful tools made a long time ago. This speaks nothing to their correctness for any period. Also I do suppose after King Gillette took over with his throw-away blades, there were scads of old razors repurposed--this was early 20th century though--so remember that if you're attempting a "period" argument.
First, please don't ruin nice examples of old SR's. Vintage steel is no longer being produced and these things come in LOTS of degrees of repair. Second, it's the hollow grinds that will be most common and the MOST susceptible to novice sharpening errors. BUT if you search high and low, you can find WEDGE shaped blades that will be very much more durable and retain their cloth-cutting edge longer than any hollow ground. Wedges have little to no hollow grinding, take a bit of effort to sharpen properly, but are quiet shaving and a legitimate shaving razor.
Also of course there are very cheap modern replicas made, and any of them could be "aged" or not and pressing them into patch knife service would probably be a blessing as I hear they're often horribly ground or totally inadequate for whisker service.
The vintage blades that take a really good edge are precious to us shavers with the blade. They don't all (no matter the make/model/origin) take and hold the same edge. Very tiny differences in heat treatment and metallurgy assure this-and there was a lot of variation in old blades.
Also, perish the notion that any settler back in the day used his shaving razor to cut fabric, ever. The edges just won't hold up to that, and then go back to a face without a lot of restoning/stropping. It'd be a waste of time and metal for a shaving person.
There's just nothing like SR shaving, but you can whack patching fabric with about anything sharpened.