You anywhere near a big box building supply store?
Buy a couple double-headed nails, with heads pretty close (you can file to size if need be) to the size of the sockets on the hammer and the frame, and ask if the have a selection of springs available(some places still have the bulk bins to paw through). Buy a couple compression type springs that will fit over the nail, but not over the nail heads. Heaviest wire you can find. And yeah, it will likely be too light a spring to work correctly, but it WILL give you some dimensions you will want to have handy when you shop for the one you will end up using.
Do you have a couple hand files? A caliper for measuring?
Is there a hole in the rear socket that the spring sits in? That will determine the maximum diameter of the hammer spring strut. There may be a slot in the front of the hammer, too, rather than at the rear. Clearance for the spring guide as the spring is compressed. If it is in the hammer, then you only need a regular single headed nail, or cut off the second head.
The two headed nail is going to be your spring guide, it just keeps the spring from bending as it is compressed, doesn't need to be anything special, other than to fit in place.
The top head of the nail gets filed to fit the slot or hole in the hammer. If there is not a hole in the bottom of the socket that the spring is supposed to anchor in, then the distance between the hammer when cocked, and the socket, determines the length of the spring guide. If there is a hole through the hammer the spring guide needs to be long enough to have the head sit in the rear hole, and the end somewhere in to the hammer itself.
Compress the spring until it is solid, and mark a little less than the distance between the cocked hammer and the rear socket, to determine the cut off length. Can't compress a spring any farther than solid, without wrecking something.
Assemble the whole lot and test for function.
Essentially, you use the holes that are there, to tell you the dimensions that you need. If you cannot find a strong enough spring, you want to know the inside diameter at the minimum, and the compressed length. You can determine how to cut of the heavier spring by measuring the wire diameter, and dividing that in to your compressed length. Lots of single shot guns out there that used a variation of a spring and a guide. Like as not, most of the hammer springs were about the same size wire and diameter, so consider scrounging up a mainspring from where you can, and fitting that along the same lines.
Anyway, it all seems kinda Bubba, but consider that if you take the gun to a Smith, you are quite able to cost yourself more than the value of the gun in shop charges, and like as not, you won't find the 'real' parts. But almost any spring strong enough will work. The rest is just in figuring out how it fits together.
The information you need is there in the gun itself.
Cheers
Trev