Shee is close. The Irish sound for "sh" is made differently from the English one; in Irish the sound is made with the tongue pointed forward near the front teeth, while the English "sh" is made with the tongue flattened and the teeth close together - the Irish one is nearer "sss", and yet is identifiably a "sh" sound.

Similarly, the English "ee" sound is also made with the tongue relaxed and fairly flat in the mouth, while the Irish sound is more forward in the mouth.

But hell, everyone will understand you if you say "shee". That's all that matters in the first place.

One of the things that's killing Irish is that everyone expects to be perfect straight away, so there's no "shaping" of one's skills from a basic skill towards a greater one.

My advice to you is say "shee" and let anyone who objects do the other thing.