If this may help here all Olympic medalists (they are counting all athletes born in territory of nowadays Slovakia or having Slovak origins)
https://sk.wikipedia.org/wiki/Slovensko_na_olympijských_hrách
Obviously, once again it is hard to count them separately, and personally I don´t think it is fair
From 1896 to 1912 athletes represented Hungary (part of the Austria-Hungary Empire)
and the best athlete of Hungarian team at the first Olympics was a swimmer born in nowadays Slovakia (Dúbrava) Zoltán Halmaj who won 2 G, 4 S and 1 B
Alexander Prokopp who won gold in Shooting in 1912 was born in Košice etc... The very first Olympian athlete of the modern era is Alojz Sokol (Alajos Szokoly) who won bronze in the 100m he had the BIB 1 in Athenes 1896 (Born in Hronec)
and from 1920 to 1992 atheletes represented Czechoslovakia
with Slovak born athletes winning 7-9-10 in Summer and 1-5-4 at Winter Games
but as I already said it is impossible to separate the Team sports medals, since the medal winning teams were composed of players from both countries For example the Football silver in Tokyo 1964 (9 Slovak players composed the team, almost the entire starting eleven) but in opposite for example the Volleyball silver team had only 2 slovaks in the roster
I think it should stay as it is, pre 1912 medals should be all counted for Hungary, the 1920-1992 should be counted for a now non-existing Czechoslovakia, and we should count only medals from 1994 for both Czech Republic and for Slovakia