I've heard stories of pigs nursing off of
dairy cows, and of pigs eating a calf as it's born, but I think with full grown cattle and/or larger calves they
should be fine. Just keep an eye on them and watch the cattle for cuts on the legs. My pigs are pretty peaceful but they're pot bellies, not bred to grow fast at all costs. Some of the modern breeds are pretty violent and dangerous. We used to visit a farm that had some sort of large white pigs and they were covered in scrapes and bruises - used to throw each other against the wall for fun, I guess. If your pigs aren't suited for interspecies grazing, you could always pen them and
feed them
lawn clippings and waste from the garden, etc. and go for a more heritage breed next time around.
As for the cattle harming the pigs, if they've had the opportunity to watch them through the
fence already there's a lot smaller chance of that. I saw some baby goats run into a field of black angus once and the entire herd of cattle chased those poor baby goats all over the place. But I've never seen cattle do that before or after, and I think with the pigs they'd probably decide they're not dangerous and just ignore them. But it would be good to stick around and keep an eye on things the first few times they're together.