Is there a way to maintain a continually updated copy of blockchain without running a wallet?
You could keep two wallets, an 'updater' wallet and a 'secure' wallet, and use the same blockchain with both using the following instructions:

Separate wallets sharing the same blockchain?

The updater wallet would run most of the time, and then you would switch to the secure wallet when needed. Heed the advice about not running two wallets on the same blockchain at the same time.