This method can be as simple as making the short hose replacements I show clear up to the elaborate rear mounted radiator system that cboy did on his lo-buck rat rod project (see https://www.hotrodders.com/forum/journal.php?action=view&journalid=17166&page=2&per page=5&reverse= , entries 181 & 182). Photo 1 is borrowed from his Journal. Go there to see the whole system, it's pretty ingenious! Rigid copper pipe is ideal for both applications because it is rugged, corrosion proof, very easy to route and fabricate.
Finish options are varied.
My favorite would be to powder coat them which would make them bullet proof and any color in the rainbow. Unfortunately, the baking oven gets too hot for the soldered joints so PC is out. You could silver solder the joints and powder coat but that requires heating the copper above its annealing point which ruins the hardness and strength. Not a good idea.
A very obvious finish is chrome plating which is what I will do to mine.
Paint is about the only other option and that will follow the same requirement of painting any other metal. Cleanliness is of utmost importance - any flux left behind will lift the paint. No functional damage - the pipe won't corrode - but it is ugly!
Photo 2 shows a paint that I have been using a lot on various things around the shop and it would be a super lo-cost finish on your copper radiator hose. This stuff gives a bright, very hard, glossy finish. I have been using aluminum color but it also comes in black, gray, bronze, gold, dark blue, light blue, dark green, light green, red, & brown. Can be brushed on to a porcelain look finish, and is just about as good as powder coating from what I can tell!
Photo 1 shows the completed hoses ready to finish and install.
One item you need to add is a 'flare' on the tip of each nozzle to keep the hose from blowing off. Look at all the nozzles on radiators and water pumps - they all have them. The way I add them is by soldering on a ring of #14ga copper wire. You can get plenty of it from scraps of Romex laying around new home building sites. Ask the foreman if you can have a couple of scraps so they won't think you are stealing! The wire bends easily around the pipe and solders on with the same technique as the pipe joints. heat the tube end from the inside so the flame doesn't oxidize the wire/pipe interface and cause the solder to not stick.
Photo 1 shows the top hose mocked up in position. Good fit!
Photo 2 shows the bottom hose mocked up. Since the fittings are asymmetric, I put witness marks on the adjoining parts so I could solder them in the correct orientation.
Soldering (photo 3) is pretty easy. All you need is a butane torch, plumbers solder and flux. sand the ends of the fitting to shiny copper, paint on a light coat of flux paste (looks like axle grease), slip the parts together, and heat with the torch. When the temperature is right, you touch the solder to the joint ad it instantly melts and capillary pressure sucks it into the joint. Keep feeding the solder until the entire joint is filled. On the upper hose, the two pipe collars came together so I did a little 'body soldering' and filled the joint flush w/ the outside of the pipe so when it is finished it will look like one solid pipe.
Your auto parts store carries straight hose in sizes up to 2" in 1/4" increments. It is sold by the inch and that is good 'cause you only need a 2" piece to make the connection on the copper pipe hoses. Photo 1 shows several pieces I have in my parts box; 1 1/4", 1 1/2", 1 3/4", & 2".
Photo 2 shows all the parts I needed to make my lower hose (top in photo), and upper hose. Photo 3 shows them dry assembled.
One item that is always a problem on a hot rod is radiator hoses. There just aren't custom hoses made for hot rods! Any self-respecting hot rodder wouldn't be caught dead with one of those corrugated universal hoses. A fall-back approach is to go ahead with a corrugated hose and cover it with a wire braid hose sheath but that always looks like someone went with a corrugated hose and covered it with a wire braid hose sheath.
So, you make a wire template like the one in photo 1 and go down to your auto parts store and walk the hose racks looking for a stock hose that has just the right configuration. Many times you are successful. Many times you are not. On my truck I wasn't.
Thus I decided to make my 'hoses' from rigid copper water pipe just like the pipes in your house. They make the stuff all the way up to 2" and even bigger and there are a myriad of different fittings that allow matching radiator and pump nozzle diameters exactly nearly every time. Photo 2 shows several of the fitting I have in the 1 1/4" to 2" diameter range. There are many more variations. One note; Home Depot and Lowe's won't have anything over 1" so you must go to a plumbing supply store for the larger sizes and style variations.
I designed my 'hose' around 1 1/2" pipe. I needed nozzle sizes of 1 1/4", 1 1/2", 1/ 3/4", & 1 3/8". Figure 3 shows how I cut and tried fittings to match the wire pattern in photo 1 and fit my lower hose.