Just so you know: a hovercraft hovers BECAUSE it applies great pressure downwards. If a 50 ton machine is hovering, it is applying a downward force of 50 tons in order to cancel out gravity.
Helicopters and airplanes force the air around their blades and wings, but hovercrafts apply force on the air right underneath the skirt. That air will press against the ground or water. It will spread through the while skirt, so usually the pressure per area will be smaller than for a wheeled vehicle of similar weight but it will still be considerable.
Also consider that many classical mines are not triggered by pressure alone, or by direct vertical pressure at all. Each kind of mine is taylored for a different kind of target, so many different triggers exist. Let me direct you to this answer in skeptics.se. Here are some excerpts:
Mine trigger/fuze methods
If we take as an example the Russian TM-83 mine this has a two-stage trigger, a seismic sensor arms an infra-red sensor that finally triggers the mine. The mine can be set-back up to 5m from the road it is targeting.
A hovercraft travelling over ground supports it's weight on a cushion of air, that means it still exerts the force of it's full weight on the ground but spread out over a larger area than a typical wheeled vehicle. Because of that weight and it's movement over the surface it will still produce sound and some vibrations that can be transmitted through the ground.
A hovercraft produces more noise and vibration than many land vehicles (Ref, Ref) as anyone who has travelled in one or stood near one can attest.
It is hard to find relevant studies of hovercraft noise, one that sheds a little light on the subject is Hovercraft Underwater Noise
Measurements in Alaska which shows that hovercraft travelling over a frozen river produce more underwater noise than snowmobiles.
As an example, a single event (pass-by) hovercraft sound exposure
(LE) of 134.1 dB measured at a distance of 78 feet is approximately equal to 14
snowmobile events at the same distance.
Although both snowmobiles and tanks (the targets of anti-tank mines) are both tracked vehicles, in other respects they are not comparable. It is therefore difficult to apply this information to the subject at hand. At the least, this study does show that hovercraft can transmit significant vibrations through the surface on which they travel.
A hovercraft also has engines that produce heat and therefore can be detected using an infra-red detector.
Type 72 mine
The Chinese Type 72 mine is triggered by a pressure of 300 Kg but is resistant to overpressure produced by anti-mine ordnance.
The skirt of a hovercraft might exert a force equivalent to less 100 Kg over the area of a mine. (Ref: "250 lbs/sf". Ref: "245 kg/m²", "202 kg/m²")
The South Koreans are known to have deployed the M75 anti-tank mine. This has a magnetic trigger.
A magnetic trigger would presumably be set off by any sufficiently large vehicle with a significant amount of steel in it's structure and with typical engine construction.
In "World Naval Weapon Systems, 5 Ed. By Professor Norman Friedman, PH.D." he says "Seemine anti-invasion … Fuzing is presumably magnetic to destroy landing craft including hovercraft" Which suggests he believes magnetic triggers in mines can, in principle, detect hovercraft.
The Russian TM-57 anti-tank mine can be triggered by a tilt-rod fuze.
Since the skirt of a hovercraft is usually in contact with the ground, it is possible that it could deflect a tilt-rod by the 25 to 30 degrees needed to trigger the mine.
The BLU-92 is related to the M-75 and can be triggerred by trip-wire.
Each side of the BLU 92 (an anti-personnel mine) has four hair thin trip wires that shoot out as soon as it lands. Ref
The air cushion of a hovercraft, and its skirts, disturb the surface over which it is travelling for at least the whole width of the vehicle (unlike a wheeled or tracked vehicle)
It may be plausible that there is a possibility that the skirt, or debris disturbed by the air cushion, will strike a trip-wire with sufficient force to activate a mine.