If you are screwing the skirting direct in to the masonry or in to wooden studs then start with drilling a pilot hole in to the skirting and the wall.
How to fix skirting boards to concrete walls.
Then we use a concrete nail and nil it into position.
Buzz the screw up with a cordless drill if the screw head just spins instead of pulling the board up tight remove the screw and put another plug in the hole before trying again.
The screws will need to sink at least 30mm in to the walls.
Use a hammer to gently tap the blade of a bolster chisel between the skirting board and the wall.
Insert a crowbar in the gap and gently pry the board away from the wall.
My only concern is with using liquid nails or silicone is that it is a temporary and easy fix.
Then we use a drill andout some noodle on.
Once the hole is drilled push a plug through the skirting into the wall and use a screw and hammer to beat it through if need be.
Find out the cause of the problem before embarking.
How to fix wet walls and damp walls.
If fixing to a masonry wall use a 6mm masonry drill bit to drill through the skirting and into the wall.
Personally in the past we have cut our skirting then liquid nailed into place.
Countersink the holes so that the screws are hidden.
For direct drilling in to masonry be sure to use rawlplugs.
Start the holes 50mm from the end of the wall and position them 25mm from the top and bottom of the skirting repeat at 500mm intervals.
If you notice damp or bulging walls it could be a red flag.
Remove any old skirting board with a bolster chisel.
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It never goes anywhere.
Place a scrap piece of wood between the back of the chisel and the wall to avoid damaging it as you pry off the baseboards.