The alternate method won't work because you'll be analyzing completely different place-and-routes, where you'll really only be running one image.
For clock muxes, the select line can generally come from:
- A top-level port
- A regisiter
- A combinatorial node based off a clock(and perhaps a combination of the previous two)
If it comes from a port, then it won't be analyzed as a clock unless you put a clock constraint on it, so you should be fine.
If it comes from a register, clocks don't propogate through registers unless you put a generated clock assignment on it, so again, you should be fine.
If it comes from a combinatorial node, then the registers/ports upstream from that comb node will not get analyzed as clocks for the reasons above, and I doubt an actual clock would drive directly into the select line of a clock mux(let me know if I'm wrong). I've analyzed numerous clock muxes without this constraint. Please let me know if I'm overlooking something.