We have performed a numerical study involving the design and optimization of InP-based microdisk lasers integrated on and coupled to a nanophotonic silicon-on-insulator (SOI) waveguide circuit, fabricated through bonding technology. The theoretical model was tested by fitting it to the lasing characteristics obtained for fabricated devices, which we presented previously. A good fit was obtained using parameter values that are consistent with numerical simulation. To obtain optimized laser performance, the composition of the InP-based epitaxial layer structure was optimized to minimize internal optical loss for a structure compatible with efficient current injection. Specific attention was paid to a tunnel-junction based approach. Bending loss was quantified to estimate the minimum microdisk diameter. The coupling between the InP microdisk and Si waveguide was calculated as function of the bonding layer thickness, waveguide offset and waveguide width. To study the lateral injection efficiency, an equivalent electrical network was solved and the voltage-current characteristic was calculated. Based on these results, the dominant device parameters were identified, including microdisk thickness and radius, coupling loss and tunnel-junction p-type doping. These parameters were optimized to obtain maximum wall-plug efficiency, for output powers in the range 1-100 W. The results of this optimization illustrate the potential for substantial improvement in laser performance.