I think Togame has an advantage. Reading her profile, she has Manipulative Charisma, is especially intelligent in terms of tactics, while Mr. Burns is openly sadistic.
She also has better reactions, at least given her ability to observe fights.
Speed: Below Average Human with
Subsonic reactions (Could accurately observe fights between Shichika and weaker Deviant Blade wielders)
I doubt she can DODGE at Subsonic speeds.
In terms of stamina, it's her:
Stamina: Ranges from Average to Low (While she managed to trek through the desert through sheer stubbornness, she normally is laughably nonathletic, to the point that she can't walk more than a couple meters up a flight of stairs and is often put to sleep by drizzles of rain)
Versus Montgomery's:
Stamina: Low (Completely tires out after running a few meters, and was diagnosed as having every disease known to man, with some having been recently discovered, through him; It has been revealed that he can die of dehydration if he sweats even a single drop)
Mr. Burns has been shown to collapse after attempting to swing a baseball bat at a man.
The key here is Mr. Burns would readily attack, & has been known to overestimate himself a little bit (Struggling to take candy from a baby or to crush an ant.), but if Togame knows she's weak, she could try to trick him into attacking and avoid him.
Again, given that Mr. Burns has collapsed just TRYING to swing a bat, & apparently still thought he was successful, as shown here
https://www.youtube.com/watch?v=s0m57ONmw8c Well....
I'd think Togame could dodge & react, or try to trick him into wasting his stamina. "Can you do an overhead swing?" "Sure, you can kill me, but could you do stand over there instead, first?"
Given her Manipulative Charisma, as her profile puts it, & Mr. Burn's overconfidence & sadism, I think she could get him to exhaust herself before she collapses.