Although it is unlikely to be an issue, it is worth checking that raising the skirting boards, by the short distance needed to provide clearance for the new flooring, will not result in the skirting impeding the doors/drawers of the wardrobe.
If that did seem likely, or even if the fitter insists that the skirting boards cannot be removed (as already mentioned above, they can be removed despite the fitted wardrobe so it sounds like your fitter is trying to minimise his/her effort required), the fitter could cut a piece off the base of the skirting board in situ using something like a biscuit jointer or an angle grinder with a suitable blade (as discussed recently in another thread on this forum - I think the thread title was "Wooden floors").