The distributor shaft that has the gear on it is lubricated at the top by grease packed into the cavity below the plastic disc- if it has a plastic disc, that is.
On some distributors the felt went on top of the grease, others had the felt on top of the plastic disc. The felt lubes the pick up coil/mechanical advance plate assemblies, not the shaft w/the gear. BTW, what I'm calling the pick up coil is the part w/the vacuum advance arm attached to it, sometimes it's referred to as a stator/reluctor. The mechanical advance plate has the pins that the weights and cam attach to. Neither one of these has access to the grease in the well or cavity below the plastic disc or felt, or both.
The grease you show should be fine. In the past I've used a lithium type grease. Wheel bearing grease (non melting) isn't a good choice- you want something that will flow when it's hot, but not be too runny. But whatever you use be sure the small feed holes to the shaft are unobstructed. They tend to clog up w/old, hard grease and always need to be cleaned out on used distributors it seems.