This is not massively helpful of me, but if flying I would look to get a really short transfer time to the location, to maximize riding time. I did Heathrow to Geneva, Geneva to Verbier (train) last September and rode for two full days. (half day Friday, Sat all day and then half day Sunday). It all worked, we caught or train connections and met the guide; but I pushed my luck timing wise and it was a long few days.
I would also look at flying with airlines that include luggage; I got a very cheap off season (well, end Sept) deal on flights (with vouchers) and ended up flying two rtn to Geneva from London for £100, which included the bike bags (was so cheap we flew Business to get the free extra bag allowance each). Train part was more expensive.
I would be interested to see where you end up, as I want to treat my wife again in 2020.