I love shrimp, but hate the draining and using paper towels to blot dry.  I now have discovered that my salad spinner does a great job of getting rid of all the water. 

Hmm, are these fresh shrimp?  When I buy shrimp they don't need draining. I'd be afraid they'd bruise or their taste would be affected.  Are yours frozen?  Perhaps that's why they're so wet..?   If so, maybe thawing them in a sieve or over a towel would work.

my mini colander for frozen shrimp. 

shrimps are too delicate to spin dry..also I do not dry mine because you loose the taste, don't you??

I agree with you, never dried shrimp either. 

like everyone says, shrimp is too delicate to survive a spin cycle in the salad spinner.  Also, I learned never to buy frozen cooked shrimp...yech.  So much better to buy frozen and then cook. 

we always keep bags of large frozen uncooked prawns in the shell in the freezer. I thaw them in a bowl of water, (takes 5 minutes) peel and place on a few folds of paper towel to dry. When cooked quickly in garlic butter you cannot tell they didn't start out as fresh prawns/shrimp. 
The shells make a tasty stock base for chowder's and some chefs dry the cooked shells, buzz in a processor and use it as 'shrimp dust'....never tried it but the foodies that eat it say it is good.
Made the same mistake buying the cooked ones and they are as tasteless as you say.