Jailbreak does not require SHSH's they are only needed for restores.
Yes you can jailbreak the IP4 on 6.01 with the latest redsn0w (recommended) it will be a tethered JB and you need to point redsn0w to the 6.0 IPSW manually prior the JB
Save your SHSH's for 6.01, although restore with SHSH is broken at the moment on 6.X history shows that you might need the SHSH's in the future!