I cant see your picture, but you will still need an aircon expert and probably a new wiper linkage fitting to stop it happening again to fix it, even if you have a mate that can do the aluminuim welding. From your comment "one side of it at least" you show an understanding of the hi and low sides of the refrigeration cycle but they ultimately form one and the same bits of pipe and if you have a leak it will all eventually be gone. You may also have lost whatever oil the compressor needs to lubricate it depending on where the leak is, the presence of oil and it's location usually indicates the site of the leak. Aircon experts use ultraviolet dye to aid detection.
Personally I'd just give the job to one man/garage that way you'll get it fixed without them blaming each other if it goes wrong again. I'd get a new hose, if its aluminium, a good welder can fix it but the slightest imperfection will undo any savings if there's another leak. Then the system will need leak testing,vacumming out and then re-gassing to the correct amount of refridgerant. You can have as many problems with too much refridgerant as too little. Sorry if that's not what you wanted to hear but refrigeration is a black art on very small systems like domestic friges and car air cons.