Only 1% of the US civilian labor force earns the minimum wage. So you're talking about a small fraction of the total US pay base. It wouldn't even remotely dent the 77% number, first because the minimum wage affects so relatively few, and second because the wages in the group are so small it won't meaningfully impact the median income that primarily drives the 77%.
To put it into perspective, by your 63% number, it comes out to about 1 million women versus 750,000 men. Shifting the pay of those 250,000 minimum wage workers (that represent the sex gap on minimum wage) by $2 or $3 probably will not even move the 77% number to 77.25%.
Close, but I don't think that quite accounts for the whole story. For instance, if minimum wage is raised, it depends on how much it's raised by to determine what % of workers will have increased wages. If we took it up to (purely as an example) $15/hr, then everybody earning less than that would also see a pay raise, but would not be included in the 1%. I don't know where you got your previously cited statistics, so I can't exactly run the numbers to see the impact, but I imagine it could be a sizable effect.
To put it into perspective, by your 63% number, it comes out to about 1 million women versus 750,000 men. Shifting the pay of those 250,000 minimum wage workers (that represent the sex gap on minimum wage) by $2 or $3 probably will not even move the 77% number to 77.25%.