The word we want to think of here is "hydraulics".
A good way to get stuff out of a euphonium/baritone/euphonium (or any brass instrument) is to flush it out with water -- which can provide a lot of force across the entire cross section of the tubing and out the bell. Just flush with a hose through the appropriate valve circuit or from the receiver. It beats trying to think of some non-damaging way of getting something mechanical in there to "grab" some object you know nothing about.
Gary Merrill
Wessex EEb Bass tuba (DW 3XL or 2XL)
Mack Brass Compensating Euph (DE N106, Euph J, J9 euph)
Amati Oval Euph (DE 104, Euph J, J6 euph)
1924 Buescher 3-valve Eb tuba (with std US receiver), Kelly 25
Schiller American Heritage 7B clone bass trombone (DE LB K/K10/112/14 Lexan, Brass Ark MV50R)
1947 Olds "Standard" trombone (Olds #3)