If it's anything like their "travel edition" shave soap bar, it's a no go for me. I find the scent of that very cheap and the lather vanishes, no matter how long I take to build it up. I relegated it to the shower but it dried my skin so much it started to get flaky - so it is now serving last gasp as a hand soap, where it is yet to hurt me... if I have any issues on my hands it will be the bin next!
But the stick may be completely different? I know the Wilkinson Sword pucks in a bowl are very ordinary, while their sticks are excellent, so it has been known to happen...