It's not like Spica only touches murderers - she would touch plenty of other people in the ordinary course of life. Which means that she'll be well aware of difference between people's outside and inside - for her that dichotomy is just normal.
And Spica doesn't have qualms about killing people that she otherwise likes (e.g. her Oshi singer in arc 2).
But... does Spica clap hands in order to check him? I would bet yes. For Spica it would be normal to check people before getting close to them. (Something that normal people also do - though through mundane means.)
Relationship? This guy would probably be a good match for Spica. He's not a murderer, so she is not a risk of having to kill him. But he's a murder otaku, so he might be okay with her murdering people. (Or he might like her even more because she's a murderer.)
The risk is that he might not actually accept her being a murderer, so he might go to the police if he finds out. But even then, Spica already told the (now deceased) police-detective that it would be okay if he turned her in.
Grandma might see it differently: She might be worried that this guy would spill the beans to the cops if Spica leaked her identity to him.
Would he leak the info? Very possible. Frankly, his personality is pretty weak. He strikes me as "All bark, no bite." So maybe... He can't handle the info, but he's too chicken to call the cops, so instead he picks an intermediate route and tells grandma. And maybe then grandma kills him to shut him up.