I always wash and dry mine carefully. It's easy. I use a paper hanky. Take hold of one corner, smooth the rest of the tissue away from the corner then twist it round and round. Now poke the thin twisted bit into the tube, push down as far as you can and rotate it round inside the tube till all the blobs of water have been soaked up. One corner will dry two tubes. For more, just repeat with the opposite corner. One tissue will dry four tubes. And dry the lids with the middle bit, pushing it into the grooves with your fingernail.
Don't forget to wash the tubes thoroughly first! My routine is empty, fill with water and empty twice, half fill, shake well and empty three times (covering with your finger is safe at this point), drain upside down till all the tubes are washed then dry as above. Lids are just held under running water for 10 seconds.
Sorry if this sounds a bit patronising, teaching your granny to suck eggs as the saying goes, but this is how I washed my glassware as a chemistry student many years ago.