2 cm shorter top tube? I think he's trying to sell you a new bike.

It would make much more sense to change to a stem with shorter reach. The one in your picture (is that your bicycle?) looks longer than 80 mm, and I'm pretty sure you could go to 80 mm or shorter.

Nitto, Soma and Velo Orange all have versions of rando bars (Nitto and V.O. also offer stems - not sure about Soma). Check their sites for drawings with dimensions.