Blackbird on an SME 3009 II

The main question would concern whether the arm was rigid enough but since you already have it why not try it?

MC cartridges generate considerably more vibration when tracking a record due to the coil moving rather than the magnet. More mass is involved and is the reason that the compliance of MCs are generally lower than MMs. That is very generalized and there are exceptions. Think of it this way, the purpose of the arm is to keep the cartridge in the grove, vibrations generated by tracking the grove are transferred to the arm, setting up vibrations in it which are then transferred back to the cartridge and degrade its ability to track the grove. The solution is to either make the arm massive or to make it rigid; either of these will make it less susceptible to the vibrations. If the arm is not rigid it will have serious resonance modes which will be excited by the vibrations of the cartridge. No arm is perfectly rigid but the better ones will be less excited. High mass means that the vibrations will not affect the arm as much as they have more mass to move. This is an extremely complicated subject and this is very simplified but I hope this is some help.

The classic match with the 3009 was Shure, but the Type V is discontinued. IF the Blackbird does not work I would try something like the Ortofon MMs, either their current range like the Blue or Black or a NOS from their classic range; these can be found on ebay. AT also makes a good range of MMs, I use one of their MCs and it is quite good , I haven't tried the MMs.