/kshe/ is most common, but it's not terribly strange to add a very brief vowel (a rare case of schwa in modern Hebrew?) there. That's what the speaker here did, and two discussion participants (mis)interpreted as an /i/.
Interesting: a great hit from 1974 starts with this word. There are two recordings by different performers, from almost the same time. Natan Cohen (or Yoram Yeruhami?) in https://www.youtube.com/watch?v=Swk4HTb7LGI sings /kshe/ (in fact I don't hear the /k/ at all, just /she/; might be a recording thing). Yigal Bashan in https://www.youtube.com/watch?v=4lRoyWot8L0 sings /k(e)she/.
This exercise now has the "slow"turtle icon next to the audio button. It's supposed to slow down the audio speed, but it just stops it.
Update: the slow turtle is gone and I really miss it. It was helpful for really long sentences if you can't hear a word halfway through and just want to play it repeatedly until that point.