What type / length of screw & plug are needed to fix wood battens (3.6cm thick) to a brick or masonry wall?

[HP79]

I want to fix a wardrobe to my wall without removing the skirting board. I've seen other people do this by first fixing wooden battens to the wall, then fixing the wardrobe to the battens to secure it. But - my skirting board is 3.6cm thick, and I'm planning to attach 2 wooden battens (each 1.8cm thick, together a total of 3.6cm thick) to the wall which is a load bearing tenement wall (either brick or masonry, I'm not sure). I can't figure out what type or length of screw would be best for this considering the considerable thickness of the wood battens? #DIYnovice
Thanks in advance!!!

 

[He who knows]

Will they be carrying any load of the wardrobe, or does it sit on the floor, and is only fixed to the wall to stop it wobbling or toppling over?