Oh. Minor detail.
You are actually asking how to securely remove a bitcoin wallet from your system (or the more extreme, remove any trace that Bitcoin was ever on a system ?)
Know that deleting a file does not necessarily delete the file (that's why they have "undelete" tools). So if you had a wallet without passphrase encryption, and then you delete that wallet.dat, there are ways of still recovering the keys. There's even a nice utility to scan your hard drive to find it:
Bitcoin private key/wallet.dat data recovery tool!
- https://bitcointalksearch.org/topic/bitcoin-private-keywalletdat-data-recovery-tool-25091