Are you talking about simply draining the 2 quarts in the pan, or attempting to do a complete drain? I have not attempted a complete drain, so I can't help there.
If you are at 95K on the original ATF, you are definitely due. I would assume you would have significantly improved shifting with new fluid. If you don't want to try to drain the entire contents, you could do a 2 quart drain 'n fill at each oil change for 3-4 oil changes. It doesn't replace ALL of the old fluid, but certainly better than what you've got, and very easy.
I just did a tranny pan drain today on my '99. Remove the drain bolt, drain 2 quarts, replace drain bolt with new crush washer, refill 2 quarts through tranny dipstick opening. When I say 2 quarts, it is approximate; measure what you empty, put the same amount back in, check the dipstick.
I would like to do multiple drain/refills but the question is where is that "drain bolt" ?
Thank