I've never been further than cleaning the shutter blades of a Mamiya shutter so know little about them. I've only looked into Compur or Prontor. A few points, though.
Should the shutter in question be lubricated? Not all types require this according to manufacturer specs. Don't be too hasty until you establish the answer.
Is the shutter clean? If not this is likely to be the problem in itself. It's not at all unusual for them to need several cleans before reliable operation occurs.
Grease may be appropriate in very very small quantities for specific locations such as a cocking rack for instance, but if it is the slow speeds that stick this indicates the problem is likely to be a dirty slow speed escapement. Depending on the shutter this should either run dry or at most may need a speck of oil on the gear bushings and pallet.
You wouldn't use grease of any kind in an escapement; all this would do is clog it up completely. I prefer Moebius synthetic watch oil for Compur escapements. Deckel recommended lubrication of the escapements in the repair manual for their shutters and they were, from memory, originally dipped in or painted with a proprietary lubricant prior to assembly at the factory. Not sure about the Mamiya items (Seiko units IIRC?).
As you will appreciate, extremely light oils tend generally to be of low viscosity and will readily flow. Thus, the choice of lubricant (if needed) should be informed and specific to the application.
The oil I use is ultra fine grade specifically formulated not to drag gears and, used in correct minuscule amounts, will not creep onto shutter blades or other components where it may create its own problems. I've used it successfully in several Rollei TLR escapements and a few Contaflice (which also use a Synchro Compur) with very good results over a couple of years now, but of course there are other alternatives. Many speak well of Nye oil, which I have not seen in Australia and cannot comment on directly. But first, please ascertain that this is the problem and that lubrication is required. It may well be that cleaning is all that is needed.
Regards,
Brett