Refinishing Shelton #9 plane handles

Hi all,

I purchased a Shelton #9 plane from a coworker awhile back. I cleaned it up and decided the jappaning was good enough for a user, looks decent actually. Now for the handles, what do you call them? The back is tote correct? I assumed they were rosewood for whatever reason, probably the redish look. Well i started sanding and.. i was wrong. From looking at pictures i think its beech? I stripped and sanded whatever was on there. The front knob looked almost black. Well I bought some minwax red oak stain and thought i would see what you guys recommend before i do this. I did the water test and there seemed to be a few dark spots that didnt want to sand out, figured the dark stain would hide it. I was planing to put tung oil finish over it, thats what i’ve got on hand. It almost looked nice enough with the water to just put tung oil finish on as it is. Anything special to know about finishing beech(if thats what it is)? All I’ve done is oak.
Let me know what you think
Thanks,
Josh