There’s a lot of different factors at play here; not all giants think alike!
First and probably most important: Was he already expecting to encounter a tiny lady? Did he cause her to become tiny? Was there some uncertainty that he would be able to shrink and/or find her?
If he set out to shrink and/or capture her, then there’ll likely be some self-congratulation at having achieved his goal. The less self-confident he originally was, the more he’s going to revel in his success. If the means of shrinking was his own invention/spell/potion, he’s going to congratulate himself for that, too. If he’s afraid of being caught and punished, then there’s going to be anxiety about witnesses, cameras, evidence, etc.
If he wasn’t the cause of her tiny size, then he’s going to wonder at how she became small (or, if she’s of a naturally small species, where she came from). If she contracted a known shrinking disease, he’s going to be afraid to touch her lest he catch it himself. He might think she’s a fairy or an alien, each of which suggest their own perils. 
He might not be predatory at all. If she seems in distress, he might want to protect her. If shrinking is completely unknown, he’ll probably think it’s important to find out what happened to her. All these possibilities will make him curious, cautious, and respectful.
Another major factor is whether he knew her before she became tiny. Their prior relationship is going to heavily influence how he feels about standing over her, picking her up, and holding her close to his face. 
All these considerations aside, holding a tiny woman in one’s hand is simply electric. Whether he indulges in it or not, it’s essentially a whole-body grope. Unless she’s supernaturally durable, holding her without crushing bones and organs requires delicacy. And she just won’t stop squirming. 
If I want my possession of her to last (and I almost always do), I’m going to keep her out of sight until I can get home. In real life I’m not a fan of being the “strong, silent type,” but if I’ve got a mouse-sized woman in my grasp I’m not gonna waste a lot of time yapping when I can just stuff her somewhere and keep her quiet. 
Please forgive the heteronormative framing of my comments. I’m as curious about the reactions female biggos (of whatever orientation) have upon encountering shrunken women, as well. 
