The wallet itself is not "updated to the block chain". It is simply a keystore for you private keys. The actual transaction type information is generally held in a software wallet on your PC/Phone in what is effectively a "watching only" wallet (ie. it has no private keys stored in it). You then use the software wallet in conjuction with your hardware wallet to sign transactions/messages when required (ie. software wallet sends unsigned transaction to hardware wallet, you confirm all the details and click "ok", hardware wallet signs the transaction and sends it back to software wallet for broadcast etc)
http://doc.satoshilabs.com/trezor-faq/index.html
https://ledger.zendesk.com/hc/en-us/categories/115000820045-GENERAL-OVERVIEW
Both of those sites have pretty comprehensive documentation explaining all about hardware wallets and how they work.