I've only used the old fashioned two-person way and speed bleeders.
I like speed bleeders. Air will get in, and a small mess will come out,
when you put the speed bleeders in, but you're fixing to bleed the brakes

don't worry about it.
Simply replacing possibly 18 year old fluid on a bike with unknown
maintenance history can't hurt, but you never know what kind of stuff
might be growing inside your calipers/lines that might not bleed out.
This is what we found inside my buddy Henry's 97 a few years ago,
he had similar milage to you:

I replaced the fluid and pads on my 97 when I got it with 24k on it back
in 2007. I just mashed the grungy pistons back into the calipers and
called it good. I missed my first Britman's Memorial Day Ride that year,
a few days before my rear brakes started hanging.
It is relatively easy to remove the calipers, change the seals, clean it
all up like new and start fresh.

Getting fluid to start going in a completely dry system after a refurb
is not as easy as cycling fresh fluid into a system that already has
fluid in it. If you used one of those pneumatic bleeders like MarkT
uses, that would work. As a speed bleeder user, I use a OEM
bleeder with a short hose connected to a syringe when my
system is all-the-way-dry, and suck some fluid into the system from
the m/c reservoir and then put back the speed bleeder and go
like normal.
-Mike