Proposed Silicon-based quantum computer architectures have attracted attention because of their promise for scalability and their potential for synergetically utilizing the available resources associated with the existing infrastructure of the powerful Si technology. Quantitative understanding of and precise physical control over donor (e.g. Phosphorus) exchange are crucial elements in the physics underlying the proposed Si-based quantum computer hardware. An important potential problem in this context is that inter-valley interference originating from the degeneracy in the Si conduction band edge causes fast oscillations in donor exchange coupling, which imposes significant constraints on the Si quantum computer architecture. In this paper we consider the effect of external strain on Si donor exchange in the context of quantum computer hardware. We study donor electron exchange in uniaxially strained Si, since strain partially lifts the valley degeneracy in the bulk. In particular, we focus on the effects of donor displacements among lattice sites on the exchange coupling, investigating whether inter-valley interference poses less of a problem to exchange coupling of donors in strained Si. We show, using the Kohn-Luttinger envelope function approach, that fast oscillations in exchange coupling indeed disappear for donor pairs that satisfy certain conditions for their relative positions, while in other situations the donor exchange coupling remains oscillatory, with periods close to interatomic spacing. We also comment on the possible role of controlled external strain in the design and fabrication of Si quantum computer architecture.