The effects of external (hydrostatic) compression and internal (chemical) expansion on the skyrmion phase have been investigated in Cu2OSeO3 single crystal and Cu2OSe1-xTexO3 (0 <= x <= 0.2) polycrystalline samples respectively. Under external pressure, the ferrimagnetic temperature T-C similar to 57 K is increased with a positive rate (dT(C)/dP = 0.27 K kbar(-1)). The skyrmion zone enclosed in the H-T phase diagram is enlarged and shifted to high temperatures for Cu2OSeO3 single crystal. Consistently, the T-C decreases with a negative rate (dT(C)/dx = -15.5 K/x) in Cu2OSe1-xTexO3 (0 <= x <= 0.2) and the skyrmion zone is suppressed and shifted to the low temperature side; complete disappearance of the skyrmion phase has been noted for x = 0.2. These observed results are explained to be related to the local crystal structure, namely, inter-atomic bond lengths and bond angles that modulate the strengths of competing Heisenberg exchange and Dzyaloshinsky-Moriya (DM) interactions. This approach to tuning the skyrmion ground state by external and chemical pressures might be useful for designing of spintronics devices.