Switching out butter for vegetable oil (like canola) when making caramels
There are some vegan caramel recipes that use coconut oil and/or various nut butters to achieve something similar to normal caramel. I haven't tried making them myself, but a vegan friend has used them for various desserts. I personally find that they can be slightly grainy compared to normal caramel, but the flavour is fine. So, it's certainly possible to make a caramel with vegetable oils. I would look up a few recipes for vegan caramel to get an idea of the correct amounts.

Side note: taste would not be my main concern if I replaced butter with oil for cookies. I would expect the cookies to just not set properly when they cooled down.