Who would the other evils be if Sauron was destroyed?
The new evils would just sprout from the seeds Morgoth had planted :
From the Silmarillion, chapter War of Wrath :
Yet the lies that Melkor, the mighty and accursed, Morgoth Bauglir, the Power of Terror and of Hate, sowed in the hearts of Elves and Men are a seed that does not die and cannot be destroyed; and ever and anon it sprouts anew, and will bear dark fruit even unto the latest days.
The new evils would just sprout from Men : it’s mentioned in the appendices of LOTR that there were still a couple of wars with Easterlings before there was peace, for instance.
And as the events in LOTR are just part of an Era that is forgotton now, we can easily think of examples of this new evil : just look at the history of mankind and what ppl did to each other (and still do). Men don’t need a Dark Lord to do evil.
Anyway, JRRT started on a sequel to LOTR where the ‘new evil’ would be a dark cult amongst youngsters, but he quickly resented the idea :
Except the beginning of a tale supposed to refer to the end of the reign of Eldaron about 100 years after the death of Aragorn. Then I of course discovered that the King's Peace would contain no tales worth recounting; and his wars would have little interest after the overthrow of Sauron; but that almost certainly a restlessness would appear about then, owing to the (it seems) inevitable boredom of Men with the good: there would be secret societies practising dark cults, and 'orc-cults' among adolescents
Does this prove that Sauron did not actually manage to fully take a 'shape'??
I think Gandalf meant that Sauron would change from a mighty Dark Lord into a pretty harmless –but still mean- ghost that likes to roam in old castles and mansions, like the cousins of Casper.
I think that Sauron would still be able to harm an individual who ran into him, but was completely unable to again form a threat to Middle-Earth. Sauron went from hero to zero.