This could be brought up in court how you are purchasing a 4.5 year old guns...might not be good should there be a looming court case involving your parenting time, from your post it appears she has custody. Depending on how vindictive your wife may be, this could get used against you. I am not sure how a judge would see this, even if the boy doesn't have access to the firearm except when being supervised.
Got a Cricket for my grand kids they loved it. Great training rifle if YOU feel your 4 1/2 year old can handle it they are only a single shot he cant go crazy with it. A few years ago I let my then 6 year old grand son shoot both my AR 15 and my Mauser. Set it up on a bench rest and sat right next to him and he did fine! But for some reason he did not want to shoot the Mauser more than once.
But he kept asking can I shoot the black gun again grandpa? I of course obliged him. Kept just about all his shots on paper at 50yrds! 
Go to Walmart and spend $10-$15 on an airsoft for you! Look for one that is the same size and has a similar "sight picture" to one of the real guns you enjoy shooting at the range. I have an airsoft target set up in my great room. I practice with it a lot and the practice does carry over quite well. It is the cheapest shooting you will ever do!
