Let’s list the basic known details for the possible solution(for the Enterprise Edition of the Sql Server that is):
– We can make the secondary replica readable and read the same data on it. (Not that you should do that by default, but if you really know what you are doing …)
– We can copy our object into the TempDB (yeah, your Multi-TB table is probably not the best candidate for this operation), or maybe into some other writable DB.
– We can write results in the shared folder between the replicas (let’s say in a text file into a File Share)
– We can export the BLOB object of the statistics out of the SQL Server
– We can import the BLOB object of the statistics into the statistics
Read the whole thing.