The cleaner fix would be to use something like a dual-outlet shutoff and replace the existing shutoff for your cold water supply to the faucet. http://www.brasscraft.com/PDF/0300_W...es_Catalog.pdf page 26 has at least one that should work.
Some plastic tubing gets brittle with age...you may want to consider replacing it as well. To use a compression fitting, you would likely need a reinforcing ferrule that slides on the inside of the tubing. Then, when you use the compression nut and ferrule, it has something to tighten down on without collapsing the soft tubing.
Maybe a picture of what you have might lead to some additional possibilities.