Have you ever watched how Edo Tensei is performed? Is so, I implore you to do so. It's not like the kinjutsu scroll Naruto used that was "an instruction guide" to learn jutsu.
The scroll is used as a tool. The Dna is placed on a particular seal on the scroll, the correct kata is performed "and by extension chakra mixture. Seals then spread from the scroll and form a circle around the sacrifice. The seals then produce ash to encompass the sacrifice, turning them into an Edo Tensei.
It is not useless, without the scroll, you don't perform the jutsu. But it doesn't inherently teach you the jutsu, just an important step.
Without the knowledge of the technique, it is useless though.
"If ET is pirated from someone (i.e via the Human Path) the person who attains the knowledge takes the spot on the Teacher-Student list of the person they robbed it from. They will then be bond to any "teacher" or "student" that the previous user was connected with." The only way you replace Tsuyo is if you stole the knowledge from his mind (Human path and mind reading technique are the most popular options.) That's pretty much how everyone has been replaced on the list.
You do that, sure go ahead and replace him on the list. But just having the scroll does not grant you it. However, if he is dead, it is a no go, as that would be unfair to Kamui.