We study the fluid-mediated impact of a deformable axisymmetric object against a rigid substrate, focusing on how its shape influences contact formation. For low approach velocities and large Stokes numbers, we show that sharper profiles (e.g., conical) maximize contact at the center and avoid fluid entrapment, while blunter ones form central dimples that trap bubbles. We also find that the resulting pressure distributions in the presence of thin viscous films can be predicted remarkably well by classical (dry) contact mechanics. These findings reveal shape as a design parameter for contact optimization in soft matter, adhesion, and elastohydrodynamics. Finally, we also theorize the possibility of a mechanical equivalence between shape and approach velocity.