Long regarded as a model system for studying insulator-to-metal phase transitions, the correlated electron material vanadium dioxide (VO$_2$) is now finding novel uses in device applications. Two of its most appealing aspects are its accessible transition temperature ($sim$341 K) and its rich phase diagram. Strain can be used to selectively stabilize different VO$_2$ insulating phases by tuning the competition between electron and lattice degrees of freedom. It can even break the mesoscopic spatial symmetry of the transition, leading to a quasi-periodic ordering of insulating and metallic nanodomains. Nanostructuring of strained VO$_2$ could potentially yield unique components for future devices. However, the most spectacular property of VO$_2$ - its ultrafast transition - has not yet been studied on the length scale of its phase heterogeneity. Here, we use ultrafast near-field microscopy in the mid-infrared to study individual, strained VO$_2$ nanobeams on the 10 nm scale. We reveal a previously unseen correlation between the local steady-state switching susceptibility and the local ultrafast response to below-threshold photoexcitation. These results suggest that it may be possible to tailor the local photo-response of VO$_2$ using strain and thereby realize new types of ultrafast nano-optical devices.