Which airline are you flying? With LX you can checkin in Davos (Platz and Dorf) already, BA as well, but you won't get a BP when checking-in in Davos for a BA flight.
I would suggest that you take your skis with you when you arrive from LHR to Davos. Because the airrail baggage transport usually takes at least 24h.

The so called fly rail baggage infos can be found here.
Even if your flight leaves late (take off-time after 19h), you must have checked-in in Davos before 11:30, which cost you a hole skiing day.
So in the end, I don't think that this rail baggage service does really make sense for you, since you are staying such a short period of time in Davos.

I don't know if there is a better solution, let's see what the others are posting