Invisible fence collars do emit a warning beep before they shock and on some models the range of the beep is adjustable.
Invisible Fence : Invisible Fence Collar
I used to work for Invisible fence and have run miles of wire through the woods. Generally we would only bury short sections to maintain the basic shape of the desired perimeter when running in the woods. It was covered relatively quickly with leaves and ground litter. In the winter when the ground was frozen we would just lay the wire on the ground and come spring, bury it in areas people would want to mow.
I would still do what I previously posted, but just lay the wire on top of the ground versus burying it. Buy an inexpensive am/fm radio to easily find a break in the wire. (It's actually a radio signal that is used to signal the collar.) Holding the radio over a known wire position, turn the dial all of he way down and the volume up and you will hear lots of static and follow the wire until the static stops. There's your break.
I' m not recommending Invisible fence over any other brand, they all work on the same principle.
I would say the hardest dog breed to train to the fence were huskies, they do have a mind of their own. Good luck!