Why not try a simple experiment with the smallest value cap, for your tweeter.
Buy the cheapest Polypropylene or Mylar capacitor you can find and do your own personal cap shootout v.s. the new electrolytic.
I did something similar to this several years ago. I pulled a pair of vintage Klispchorns out of storage. One worked fine, the other... there was no tweeter output. Traced it down to a bad capacitor. (1uF or 2uF, I forget which) Just to prove things out I ran down to Radio Shack and got a cheapy electrolytic, popped it in, and the tweeter worked. Later when I went to rework the crossovers , I used Solens purchased from parts express. So ultimately I was able to compare the original oil capacitor from the 'good' Klipschorn, a cheap electrolytic, and a Solen. Frankly, I couldn't tell the difference in sound.
I'm not sure I understand when people mention about designers 'voicing' the speakers using specific capacitors. Is this true, or just some folklore that keeps getting repeated over and over? I tend to believe it's the latter.
Has anyone actually talked with a designer who claims to have 'voiced' a speaker using a specific type and brand capacitor? Or are they just assuming this was the case?
Other than maybe super high end manufacturers, I'm thinking the designers designed crossovers using what was budgeted for, that being, electrolytics. I don't buy that they insisted on a certain brand, but probably what they got the best price on. And if that supply dried up they'd use a similar product from another manufacturer as long as it met basic specifications.
Interesting that ConradH finally mentioned something that few do. The fact that drivers change over time. So.... even if you hunt down those elusive original capacitors to retain the so called 'voicing' , it's not gonna' be the same as original. So maybe the better capacitors will somewhat offset that or, just as possible, they might make it worse.
I think there is a case for using the better capacitors as the film/foil and poly caps (if I'm to believe what I hear) tend to last longer, stay in spec longer, and have a lesser failure rate than electrolytics.
Just my $0.02