No, you do not have to be able to jump to hack.
As long as you are safely attired ie, boots, jodphurs or tracksuit bottoms, hat, gloves and possibly a body protector and you can walk and trot safely you are okay to hack and it is a good thing both for you and the horse to explore the countryside and get to know each other better too.
Even totally inexperienced riders go pony-trekking which is what hacking essentially is.
The thing with hacks is to keep your eyes open for potential scarey things like plastic bags etc, where your horse is going - ie, not into water of unknown depth, but the horse will usually tell you if this is the case, they have a sixth sense, and not into wire or something. If you are not sure of the footing, find another route round.
Keep a good contact on the horse's mouth so he does not slop around, keep your wits about you and ride normally and be sensible and considerate of another rider and other users of the bridle pass - don't go galloping past walkers, dogs etc.
I think you will be fine on a steady hack.