I have the episodes on my computer so in a pinch I could try recording the clip but the actual playing is interrupted a few times by the actual plot of the episode and cutting away to Filia and Lina fucking around with some haunted pottery, which is kind of distracting and probably why there isn't an actual clip on youtube.

That said I vaguely remembered someone uploading the soundtrack version onto tumblr and, well, I was sort of right- it's a cover, but I can confirm from listening to the show that this cover is the right tune. And looking up "slayers sasurai" on youtube gets you a few other covers or the song edited over pictures/clips of Zel. And all these videos are from 15 to 9 years ago, lmao