All good advice here especially the ones that said:
1) Just take him.
2) Make it fun, kids have short attention spans.
I’ll just add that you and your son are welcome to come shoot with me and my boys at our place. They’re 8 (twins) and I have a Cricket rifle you can use.
I'll agree 100% and what a generous offer. I started my son with a crickett now he has a ruger american rimfire.
And add to:
Clean/ handle let him handle real guns to take the mystique away. You have him check or you show him you're checking that the gun is unloaded and safe to handle.
Don't force it. Stop when he wants to then ice cream, sno balls, whatever.
Also have you considered a bb gun? Hang ballons on a line and you 2 take turns popping them.