How can a single person operation keep a collection of online wallets secure?
This is a great goal, which many people will assume just can't be done.  But remarkable strides are being made in the field of secure cloud computing via homomorphic encryption.

These schemes allow servers in the cloud to perform computing tasks (currently only a limited set of arithmetic) on encrypted values without decrypting them.  See more at In what ways does Full or Partial Homomorphic Encryption benefit the cloud? - IT Security - Stack Exchange

A question about applying this to Bitcoin clients on Less Wrong is here: Homomorphic encryption and Bitcoin but they seem to be confusing homomorphic encryption with a form of secret splitting between two computers, which would not meet the goal outlined here.

I'm guessing that current homomorphic techniques are inadequate or too slow or both for bitcoin, but I'm not sure.  But further research may make it practical.