I do not think there is a wallet that can sent 1000 satoshi most of the wallet the minimum transaction is 0.001 or 100k satoshi. Just to clarify 1000 satoshi or 1000 bitcoin?
If 1000 satoshi you cant find an option to send that just wait to make it 100k sat then you can start the transaction!
1000 bitcoin is a huge amount of money it wont carry by some wallet it would be suspicious transaction that may developer will trigger on that transaction to hold and verify it.