Hmm, I'm not sure what the best bet would be for a chick that size. The second chick, the one we culled, was much younger than yours, no more than a week. For that one we used sharp kitchen shears, quick and as painless as we could manage.
Yikes, that's a really severe cross beak! Whether you keep this bird really depends on how much time you have to tend to special needs. A cross beak that severe is going to negatively impact quality of life. It's going to be a struggle to get enough calories to maintain body weight, you're...