The idea you have is not a bad one - rather than investing in mining hardware that takes days to arrive, just do it "on the cloud".
But be careful - you can't guarantee the person running the mining hardware will be around to service their machine constantly. What if they take a vacation and their Internet connection is interrupted and the mining program crashes? Or what if they are evil and just run away with your money?
Especially when it comes to Bitcoin, never trust people unless scanning reddit shows that they are probably trustworthy.
Your best bet would be to use a trusted site to mine with "mining contracts", like
ghash.io. In light of recent 51% attack paranoia, maybe it's better if people stay away from ghash.io but I'll leave it up to you to find a trustworthy seller of mining contracts.