I did a little Googling because I was not familiar with liquid paraffin. It looks like it is similar to mineral oil in the US. Drugs.com says it has a shelf life of 3 years unopened. Some sources cautioned that when using it as a laxative with pets, you should mix it in with food so that it isn't accidentally inhaled into the lungs.
A lot of people here are fans of adding a little bit of canned pumpkin to the cat's food. The fiber in the pumpkin helps them pass the hard stool. Miralax can also be used for the same purpose.
Petroleum jelly or OTC hairball remedies can be used as a laxative, but not long term. The oil coats the digestive track which helps pass hairballs or hard stool but can interfere with the absorption of nutrients. Paraffin oil would work the same way.
Dehydration can cause or exacerbate constipation. Make sure your cat is getting plenty of water. Cats who eat primarily dry kibble are much more prone to dehydration. Wet food is better for your cats for a lot of reasons, so if you're feeding mostly dry food, you may want to consider a diet change.
Also, make sure the litter box is kept nice and clean. If the cat doesn't want to use the box, they may hold it, which can lead to constipation as well as urinary track problems.