LV's motive / timing for Draco's mission

[Hagrid]

No: HPFGUIDX 138797

When did Dumbledore injure his hand in relation to Snape hearing of 
LV's plan?

If Snape knew LV's plan before Spinners End, then was it before DD 
came to him to be cured after blackening his hand?

Snape could have killed DD at that time, or disarmed DD and 
summonded Draco.

OR-

What is Snape reported of DD's Dark Curse encounter to LV. You-No-
Poo could have decided DD was too dangerous to keep alive then.

LV may realise DD got the ring from his uncle's old house, but know 
that DD doesn't know how many other Horcruxes there are. The only 
one with clear information was Slughorn.

Therefore, it was no coincidence DD went looking for Slughorn to 
bring under his protective wing at Hogwarts.
-aussie-