In the mean time the broken piece can not go anywhere, So unless you are low on fluid there is no hurry to any of this.
Another interesting bit of trivia is that through the various trannies the dipstick tubes change with every application and the stick doesn't. This generally means that while the tube from a 300E won't work on a 300SEL, the dipstick probably will.
Bosch Master, ASE Master, L1
33 years MB technician