So far my understanding, you cannot do it using any single tool/action. You may need to use python and use the the following hints:
use search cursor (descending order by shape area), since you said 90% or more area contain means, your one polygon's 5-10% buffer will cover 100% contain, and selected small polygon can marge/delete with the larger one. this way the all polygon loop to solve ....
Funny, but might interest you.