这是个习语，其中should可能强调“惊异”的情绪。

1. 参见韦氏词典。

what/who should someone see but

idiom

—used to say that someone is surprised to see something or someone

I looked up and what should I see but a hummingbird right over my head.

They were walking along when who should they see but Kim!

2. 参见朗文词典。

what should I see but something/who should appear but somebody etc

used to show that you were surprised when you saw a particular thing, when a particular person appeared etc

Just at that moment, who should walk in but old Jim himself.

值得注意的是，最后一个例句使用了句号。