Download the latest version of RedSn0w from the Dev-Team's site. Download the iOS 6.1 IPSW for your iPhone 4, make sure that it matches your iPhone in terms of band (GSM or CDMA). Open up RedSn0w, click on Extras, click on Select IPSW. Point it to the iOS 6.1 IPSW that you've downloaded. This will now create a new IPSW.
The IPSW that you've downloaded will start off with
iPhone3,1_6.0.1 or iPhone3,3_6.0.1
The IPSW that you've custom made will start off with
NO_BB_iPhone3,1_6.0.1 or NO_BB_iPhone3,3_6.0.1
Put your device into DFU mode, and restore it using iTunes by pointing it to the NO_BB IPSW that you've custom made. This will preserve your baseband and upgrade your iOS 6.0.1. Make sure that it's the NO_BB IPSW or you baseband will upgrade.