You are making a small thin disk , 18mm (0.7 in) diameter is what Berea`s website suggests (I prefer 20 mm , although that requires a larger chamfer on the underside to allow it to seat ) , with a thickness of 30-50 thou at the center , tapering to 5-10 at the edge . That usually requires stabilized or CA hardened wood especially if cross grain , or plastic . It also doesn`t allow much room for error when using typical pen blank cutoffs .
There are 3 ways that I know of to make them . The first is to use a 3 or 4 jaw chuck to hold a square or round or irregular full size blank , turn to the desired diameter , shape the end as you wish , sand the end , part off the disc , and repeat . Some parts will end up in your scrap bin . Overall conversion efficiency depends on your skill , size of parting tool , tool sharpness , and luck .
The second way is to take your small pieces , cut them about 0.1 inch thick with a thin kerf saw , sand one side a bit , attach it to a face plate with 2 sided tape , and carefully turn it down to size . The tape does not hold well if it gets too hot , and thin wood does not have a lot of heat holding capacity . Both turning and sanding can generate quite a bit of heat .
The third way is to take a small piece as above , attach it with 2 sided tape to a dop stick of the desired finished diameter , shape the piece on a face grinder (watch the heat) , then finish sand by hand with the piece still on the stick .
Wouldn`t bother with the tiny little chisel . Regular tools , but SHARP .