The train ticket is 30 dkk less to Skanderborg than to Silkeborg. A taxi from Skanderborg to Vrads Sande will cost approx. 240 dkk, Tell the driver to go to Vrads Sande. The drivers go by meter. The normal taxi takes 4 passengers.
Larger taxis exist, but they are normally only available by ordering in advance.
If you buy your ticket to Karup, you have to go to Copenhagen and pass through customs there. There is a free bus service between the international and the domestic airport in Copenhagen. Take the domestic flight to Karup. You cannot cheek in your luggage from abroad to Karup. Karup is approx.