I have to be 100% honest, the words "toddler" and "really wants a gun" sort of made my jaw drop. I think "turning 4" doesn't really rank a child much higher than 2 or 3 from a maturity standpoint, though I applaud your desire to want what's best for him at this age. I think the truth is~he's simply too young to shoot anything "real" responsibly, be it an airsoft, BB gun, lead pellet gun except under the most strict supervision and if that's the case, I wouldn't get too hung-up gun weights/difficulty of cycling the action etc. You'll be doing that for him anyway.
I've been down this road with all 3 of my kids, 2 nieces, 3 nephews, and allot of their friends and I've learned allot about attention span, what to expect, etc. Everything from archery gear, slingshots, air rifles (BB and pellet), air pistols, airsoft, Cooey 39 22, Cooey 75 22, Savage Rascal, etc. etc. Out of all that, I've learned;
1. Attention span even when everything is going perfectly~VERY SHORT
2. The Savage Rascal and a CO2-powered single shot .22 air rifle~both the biggest hits. Why? Scoped, right LOP, easy to load, shot off a rest at close range reactive targets, not loud.
3. Ammo for 22s~always the most quiet, only make sure the scope is zeroed for it. Used to be only CB longs, but now CCI Quiet-22...even Aguila Colibri. No matter what gun/ammo combo~eye and ear protection
4. Targets~reactive targets only, kids don't care about tight groups. Popping balloons, gongs that go "ting" when they're hit? That's a different story!
I have a bouquet of lever action BB-guns leaning in the corner of my lock box. I've always had a soft spot for them, could never get any kid excited about them. Maybe a watchful parent/uncle takes the "mischief" thrill-factor out of Daisy BB gun ownership. lol
Anyhow, not judging in any way/shape or form..just suggesting the little fella maybe ought to be using your gear with you helping...and that something like a Savage Rascal would not only fit his physical size, but he'll be able to operate it himself under strict supervision. Accurate little rifles too. Once scoped, if he's still keen a couple of years down the road, you can run faster ammo through it and the satisfaction level should still be there. When my daughter hit 12 and got her hunter's apprentice license, it's our green Savage Rascal she wanted to take when I visited a farmer friend to rid his barn of pigeons. I had at least 1 other 22 that fit her better (Anschutz 1450) but the comfort/ability level with the Savage was very bad news for the pigeons. 5 years later, that same farmer still tells me how amazed he is at how she never missed. My kids now range from 5'2"-6'4" and they won't let me sell that Savage Rascal. I suspect I'll be teaching my grandkids to shoot with it.
Good luck, and safe shooting no matter what you decide.