That board is actually two separate boards that have been glued together. When one of them was ripped (i.e. cut lengthwise) it went through the knot.
You can see that along the entire length of that slat none of the grain flows through that seam.
I don't think doing a sawdust + epoxy/shellac/glue filler will sit well with an oil finish
Actually they're fine. Fills don't have to absorb the oil in the same way as the surrounding wood, especially very small fills.
I hate to recommend it but this is a good candidate for commercial wood filler. If you have one on hand that's a colour you could live I ...
Should I look for another way to fill the void?
This is a matter of opinion but I don't think so. Epoxy is one of the best, if not the best, materials to fill voids and fallen knots. It has become virtually the default choice for this purpose for this reason.
It should be mentioned that a void at the edge of a board does represent a significant weak spot, ...
It's a knot. Or at least you are treating it like a knot. Knots don't match final finish color in virtually all cases.
The basic approach - fill with black epoxy. Trying to be subtle but it won't match - fill with a dark gray epoxy. Tossing subtle out the door, fill with epoxy and turquoise (or whatever) chips, polish it up & make it (more of) a feature....