At first not, but later Sauron interestingly did use lesser minions for the task of finding the Ring. After the defeat of the Nazgul he chose not to send them directly against the Fellowship, but to keep them hidden, and have them command a group of orcs led by Grishnakh. Even in this case it was not a large group, but only a small taskforce. Throughout Grishnakh's mission he was constantly instructed by the Nazgul, showing that Sauron still hoped for secrecy. He could have sent a large host, and that might have actually been better in the end, but he wanted Rohan and Isengard to know as little about this as possible.
Probably this was the wrong decision, sending the Ringwraiths would have probably meant death for Eomer and his men, and who knows if Rohan would have been so strong afterwards...but that's another story.
Anyway, sending the Ringwraiths seems the best solution, since unlike Orcs they could feel the presence of the Ring, and in the beginning it was only they that could find it easily despite its unknown location.
Also, other minions would never have received such helpful information from Saruman as the Wraiths did (UT).
And I am not sure what you mean by attacking key targets?
MoS and archers on horseback attacking Hobbiton? lol
...funny but inefficient