I'm gonna take issue with the wooden bat. I have yet to see a 7 year old, no matter how athletic, who could put a good swing on a wooden bat -- one which is long enough to cover the strike zone.
It's easy to find aluminum bats like the one mentioned in the OP: 27" and 17 ounces. An athletic strong 7 year old can swing this, and have good quick mechanics while doing so. A similar length wooden bat would weigh 7 or 8 ounces more.
I'm an old f*rt, and in the mid 50's, the youngest age which Little League accepted was, I believe, 9 years old. Where I lived, the standard age to begin was 11, although sometimes a 10 year old with excellent athletic ability was allowed to play. Why so late compared to today? Well, the bat I started with was a 30-30, and as I recall, the lightest bat available was 28-28. We could swing those bats at a younger age to play softball, but we sure couldn't make a good swing against even a 50mph pitcher until we weighed a hundred pounds or so.
I believe that at age 7, a kid will learn better swing mechanics with a sub 20 ounce bat. And the bat needs to be long enough to cover the plate; otherwise the batter tends to extend his arms prematurely to reach the outside pitch. Aluminum fits the bill.
What age to start swing wood? Whenever the player can handle an aluminum -3 in game situations, then he should be able to handle a e.g. 31" 29 oz. wooden bat (which is quite a bit harder to swing) in practice. Typically 13 years old for talented young lads.
Obviously, your mileage may vary....