No to rabbits as pig companions (many reasons- they eat different foods, pigs need Vit C, rabbits eat a tiny amount of pellets and loads of grass/hay. Rabbit can injure or kill a pig with a kick. They can bonk it. Your shy pig will be terrorised by a huge rabbit. They carry a respiratory bacteria that can kill rabbits. They 'speak' rabbit - it would be like me being forced to live with someone who speaks only Cantonese )
So pig alone:
How old is he?
You can introduce another pig but your best bet is a very young boar. It's not a 100% guarentee that they'll get on but providing you do it properly, it can work.
Or you can ask a rescue to boar date him. They may have a single affable boar adult?
We boar matched our adult boar when his brother died. We got a 6 week rescue boar. They were lovely, the odd rumble as the piglet grew and took over, but nothing nasty.
When the piglet was a year, the older boy died.
We didn't feel a young boar would be safe with our huge (3lb) sex-pest (he spent a fair amount of time jumping on his older cage-mate and being told to "Do One"
We got two adult rescue sows (same age) kept them side-by-siding while the boar was neutered and his 4 week waiting for sterile phase.
They get on well, the sows are feisty and take no prisoners
I did ask the Rescue for stroppy girls .
Short haired bigs are much less effort I agree and IMO , the more 'bred' they are , the more health problems. A good solid smooth (like our girls) or a Rex (like our boy- but my DD is allergic to his fur)
A Rescue might have a neutered sow. Less common than boars to be neutered.
Our boar was a year old , they need to be fit and healthy to be neutered if that's the option you choose, but it's not taken lightly.