Funny you should start this thread, I'm also in the process of replacing a radiator on my 1800. I cracked mine while removing the front fork and dropped it on the darn thing. Tried to fix it but to no avail. I went ahead and ordered a new one. You might try and take yours to a radiator shop and see if they can fix it. But if they can't you can order one online from either HDL or CheapCycle Parts.
Removing and replacing is not that big a deal. Just get a container that will hold at least 3 quarts of fluid and remove the bottom hose. It's best to loosen the radiator first then pull it off the hose. Don't squeeze the nozzel because it's very soft aluminum and will bend. Drain out all the old coolant and wait for new radiator to arrive.
Other than the radiator itself you'll need to get a new o-ring for the sensor plug at the bottom of the radiator. If it's the same size as the one on my 1800 (which it may not be) you'll also need a 22mm deep well socket to remove and replace it. Be sure to save all the bushings and bolts from the old one , you'll use them again.
After installing the new one you'll need to flush the system with distilled water and drain and then add the new coolant. However you could go ahead and flush your system with the old radiator since you gotta take the hose off anyway. I did.
It's a bit of a pain because the filler cap is under the tank and requires removing and replacing the tank a couple of times. My 1800 uses the 50/50 pre-mix sillicate free coolant. I'm assuming the 1300 does as well. Oh and there is a drain plug at the bottom of the water pump behind the transmission cover, look for the bolt with the copper washer at the 6 o'clock position. But if you have to pull the hose anyway it's easier the drain the system that way.
Several threads around here on the procedure for changing the coolant. Be sure to search and read them. Your 1300 may be different than mine is some way.
Now after all that, check your hoses first, most of the time it's just a loose clamp. Use a ratchet and a 5mm socket and tighten those clamps down and see if it still leaks.