Well,
I would advice now to be little patient and wait, if the tree will recover...
So, do no prunning, until new shoots emerge...
Just give the tree a couple of time, to settle and regrow... if the roots are healthy, it would not get worse and maybe new shoots will start growing....
Just be patient...
About the black widows: Well, as far from my knowledge those spiders are dangerous... but... slamming them with a shoe won't be surviveable for those...
So, if you want to kill em, just get them of, to the ground an kill em just stepping onto them. Their venomous claws won't get through leather or the thick rubber sole of the shoe....
Otherwise catch em with a glas and hand it out to someone wo takes care... and a spider-ex does not often have a non-visible effect on spiders, they take a sniff, grin and live, as nothing might happened....
So if you will killem, sqeuzzing to death is very well....