To accomplish the desired effect,
I'd stain the pieces first, then install the plugs.
1. stain your desired pieces.
2. install the unfinished plugs.
3. cut the plugs flush, using a small ''flexible flush trim saw''.
NOTE: the flush trim cutting teeth on this type saw, have no saw-tooth set, the teeth are flush with the saw blade thickness, and will not scratch the finished surface.
4. ''if necessary''--- sand the plug ends, using a short section of 1/4" dia dowel rod---
glue a 120-150 grit piece of sandpaper to the end of the short dowel rod---
cut the sand paper, flush with the OD of the dowel rod---
the result should be that the sand paper will be affixed to the end of the dowel rod, and not extending out from the edge of the dowel rod.
5. while sanding the plug ends, using a slow back-and-forth motion or a rotating motion; akin to using a pencil eraser---
this can be accomplished by hand or chuck the short piece of dowel rod in a slow rotating drill.
ALTERNATE METHOD: A small screw can be placed in the end of this short dowel rod---opposite the end with the sandpaper.
Remove/cut off the head of the screw---chuck this short dowel rod, with the screw fitted into an adjustable chuck of a dremel tool. The right angle accessory, for the dremel is especially handy for this task.
Apply ''light'', soft touch, sanding pressure to the end of the plugs, to obtain the desired smooth finish.
6. Stain the ends of the plugs, to the desired colored, using a small artist brush.
WORKS FOR ME.
A short piece of dowel rod, can be affixed in a hex-nut driver---secured in place using hot-melt glue---secure the short piece of dowel rod into the nut driver.
Using the nut driver in a rotating motion, to accomplish the rotating sanding task, to the plug ends, to make smooth.
TIP: applying masking tape, to the adjacent finished area, so as to prevent scratch/sanding marks.
Apply the tape over the plug---cut the tape away, over the ends of the plugs, using an exacto pointed blade knife tool.
I haven't tried this but after gluing and staining the plugs, you could seal them with CA (super) glue before staining the oak. I would test this first because not all super glues are the same.
Instead of using oak plugs why not try using plugs made of maple or even the paint grade plugs
Also u could drill a pocket in scrap wood put dowell in cut and sand it .Poke it out from back and go to next one until all are cut then after that stain is dried put plugs in and its a done dea.I have a VIDEO ON YOUR SITUATIONl