All-optical switching of 75 fs pulses centered at 1560 nm, driven by 270 fs, 1030 nm pulses in a dual-core optical fiber exhibiting high index contrast is presented. The fiber is made of a thermally matched pair of lead silicate and borosilicate glasses used as core and cladding material, respectively. The novel switching approach is based on nonlinear balancing of dual-core asymmetry, by control pulse intensity induced group velocity reduction of the fast fiber channel. Due to the fiber core made of soft glass with high nonlinearity high switching contrast exceeding 20 dB is reached by using control pulses of only few nanojoule energy. The optimum fiber length is 14 mm, which closely match the calculated coupling length at the signal wavelength. The results express significant progress in comparison to similar studies based on self-switching of solitonic pulses in dual-core fibers and represent high application potential.