Not an expert here - but the first 90 seconds or so of that Sound of Silence recording has no strong rhythm and no climaxes. From my very personal point of view skating is a form of dance, and needs rhythm to be interesting and properly assessed, and climaxes (which tend to emphasize emotion) might occur at the points of your program you want to emphasize (e.g., jumps, spins...). You could cut out the start...
But it is beautiful music, performed very well.
I admit that if you don't maintain a consistent rhythm, music with a strong rhythm might be a mistake. For that matter, it might also be a mistake if performed in a place that doesn't have a well synced music system, that delivers the sound simultaneously to the skaters and judges, which is somewhat hard to do in a space as large as an ice rink. You more or less need many vertically directed speakers on the ceiling, with built in timing delays that take into account the distance from the ceiling to the listener. AFAICT, most ice rinks do a pretty bad job of that, in part because it isn't what most hockey fans want.
The 2001 theme music (Also Sprach Zarathustra, by Richard Strauss) is beautiful music, but yes, it stops early. And if you continue on with Strauss's next movement, it isn't similarly dramatic. So you'd want to continue it with something else. How about Darth Vader's theme music?
https://www.youtube.com/watch?v=-bzWSJG93P8
Though it's kind of masculine.
But would you instead want something that expresses your personal program, costume and skating style? E.g., A performance take of a soloist from
Harlem Nocturne, one of my favorite saxophone pieces, could be wonderful, by my lights - beautiful, lots of emotion - but you'd need a provocative look, costume and skating style to carry it off. (You say you like lyrics. There have been lyrical interpretations of Harlem Nocturne, but I don't know any with the same sexy feel.)
Or how about "If I had a heart" from the Viking TV series:
https://www.youtube.com/watch?v=8YyTWzb4_sw
(maybe find a performance that brings out the words better - or cut back on the bass)
Of course that's a completely different emotion, and needs a much darker costume.
I loved Celtic Woman's music. E.g.,
https://www.youtube.com/watch?v=z-ttrQ38mOc&list=RDz-ttrQ38mOc&start_radio=1
https://www.youtube.com/watch?v=Yfwlj0gba_k&list=RDYfwlj0gba_k&start_radio=1
Again, lots of emotion.
Could you carry off young Wednesday Adam's Dance music?
https://www.youtube.com/watch?v=NakTu_VZxJ0
That show had other cool music performances, e.g.
https://www.youtube.com/watch?v=S523q5PCX6Q&list=RDS523q5PCX6Q&start_radio=1
Anyway, that's just my take: find something special and unique, that carries real emotion, that you can express artistically, not something too generic.
But maybe other people disagree... I'm used to that.