Shipping compiled shaders is a feature request that pops up from time to time in gfx-rs land [1]. So far, we have been skeptical about this. Something like a serializable pipeline cache would help, but not entirely solve the shipping binary size. Although, is it really important? "Hello Triangle" may be a few megs, but the code for shader translation is a constant addition to it, so extrapolating this 5.2Mb value is not useful.
Currently, both Dawn and wgpu-native use SPIRV-Cross for translation of shaders. The plan is for both is to migrate to in-house translation. In case of wgpu, that would be Naga [2]. Sometime in the future, you could be able to include it with only WGSL -> AIR (Apple's shader IR) code path compiled in, without anything else. Could be good enough for the code size? :)
[1] https://github.com/gfx-rs/gfx/issues/3117
[2] https://github.com/gfx-rs/naga