Unless the gun was owned by your family and has historical value to your family, or is a very high grade gun, what you are describing is a bottomless pit that you will throw far more money than it will ever be worth at, for a gun you don't plan to shoot.
There is a gent selling a whole stack of parts for these guns right on the for sale part of this website. He is a gunsmith. I'm not sure why he wants to sell all his parts for this style of gun, but, you might ask him if he has what you need, even up to a complete stock for the gun. He might be interested in helping you with your project, as well.
There is also an individual who posts here who will tell you that it is impossible for the wood or any metal parts on your LC Smith gun to be broken, that it is the finest example of it's type, engineered to be flawless and perfect, and that you must be badly mistaken about it being broken, because they never break, but, if it is, there are only two or three gunsmiths on the face of the planet who can fix it, and you should send it to one of them.
Reading his posts on the subject of LC Smith guns is just like reading a George Herter catalog from the 1960s. You'll know them when you see them. Take what he says with a grain of salt.
And, good luck. We are at a time when it might be cheaper or more prudent to simply find a better example that you could actually use, saving the first one for parts.
Here is a link to the ad:
http://www.doublegunshop.com/forums/ubbthreads.php?ubb=showflat&Number=520192#Post520192He is well regarded as a gunsmith. I have never used him, but, would, should the need arise.
Best,
Ted