A pickup with cattle racks is just fine for picking up small animals. I have, with a bit of help from my partner, wrestled a full-grown ram into the back of a pickup truck for a vet visit, so that's doable as well. I wouldn't even try to wrestle a full-grown pig into the back of a pickup. No way, no how. The first year we raised pigs, we tried to train them to walk into the back of the truck for transport to slaughter. Don't even get me started. Maybe if we had started two months before slaughter date, and had a better ramp. The pigs were freaked out about every single part of that operation: stepping onto the ramp, walking up the ramp, standing in the truck. If you don't have a proper loading chute, with walls that block out the view to the side, I wouldn't try getting pigs loaded in a pickup. The other thing I would try is, if there was a ledge or berm I could back up to, then I could probably get the pigs to walk in. What we do is, park the trailer in the field the last two weeks of before slaughter and stop feeding the pigs anywhere except in the trailer. One of them is usually up it the first day. And one of them usually holds out for as much as two full days. But they end up trotting up it like champs. They still don't like the ramp, but it's much lower to the ground than the truck bed, so it's much less steep.
EDIT TO ADD: The reason it works with a ram, and not a pig, is that with the ram, you can kind of grab him by the neck, then kind of shove his upper body onto the truck bed, then while one of you holds him there, the other one can kind of pick up his back half and shove it up too. If you are physically capable, you may also be able to scoop him around all four of his legs and sort of shove him up into the bed. I've done that once. None of these approaches work on pigs, though. You can't grab them around the neck because they just wiggle out. And you can't scoop them around their legs either. You can kind of grab them around their chest, but then they are screaming and wiggling and maybe even biting, and it's just not worth it. Also, a full-grown pig is going to weigh at least 100 lbs more than a full grown sheep.