For me, I define influential for a sport in terms of gaining legendary status outside of the actual skating world - which is small, be the first AND be able to do other things based on their athletic performance with a Michael Jordan type flavor... Granted, my list is pretty much modern era because I don't know enough about ol' school skaters (ala John Curry) to have an opinion, but when has that ever stopped me?
My list includes - in no particular order:
Ladies: Michelle Kwan, Kat Witt, Kristie Y, Sonia, Dorothy, Peggy, Debi Thomas, Tonya Harding (lots of firsts with this one...) and by extenstion Nancy, Midori Ito and by extenstion DivaKwara (mainly because of their ability to ignite a country's imgination for a sport - Mao, Miki and the rest need to move it to the next level). I don't know enough about Russian ladies to make an educated guess about Irina nor am I certin if human interest in her ability to win despite obsticals is enough to make her influential vs. simply cooler than the average bear...
Men: Dick Buton, Brian B., Scott Hamilton, Kurt Browning (mainly because he made sucha statement about not letting the OGM define you), Toller Cranston
Pairs: Sergi & Ekateria
Dance: Torvell & Dean
Cheorgraphers: Tatiana and hopefully Lori Nichols (mainly because I love her...)