Why do you suggest avoiding veg oils?
PUFAs are inferior to saturated fats when it comes to boosting HDL. They also break down under heat and produce dangerous trans-fats, which saturated fats do not.
Vegetable oils would have a shelf life of just a few weeks except for the extreme processing they go through involving very high heat. Technically, they are "rancid" as soon as they're bottled and they have to add deodorizers so that won't be obvious to the consumer.
They are basically untested as they have only been part of the human diet in this form for a very short period. Remember corn oil the "great savior" (from that evil saturated fat). Don't hear so much about that any more! It turned out to be a disaster.
Many times they are found in hydrogenated form - another public health disaster (NEVER, buy "no-stir" peanut butter!)
If you must have a good fat which is not "saturated", olive oil is good, but only cold. Unlike the saturated fats, it is not stable under heat.
Coconut oil is probably the best all-around oil on the planet.