Kolmogorov complexity has the exact same problem (if it is a problem) as length-after-LZ-compression: what maximizes the complexity for a given length of string is random junk, which seems a long way from what people normally mean when they talk about "information".
What creationists are trying to get at when they make claims like "mutations never add information" would, I think, be better expressed by globally replacing "information" with something like "usefulness". Of course their claims are still wrong when you make that change (mutations usually don't add usefulness, but occasionally they do, and natural selection filters that to produce a steady increase in usefulness), and often the use of pseudo-information-theoretical arguments is just flimflam, but the Instant Refutation of saying "mutations almost always add information" or "duplications almost always add information" or whatever doesn't really engage with what the more honest ones are trying to say.
You could say that at DNA level a mutation can contain the exact same amount of information as a non-mutation if you use Shannon's measure e.g.:
GTTACA
to
GAATCA
would be the same. But of course there is a vast difference in terms of the phenotype that would happen from this mutation (if the mutation happens in the relevant area).
Of course strictly speaking you can also add a mutation, the most trivial example is:
AAAAAA
to
ACAAAA
Obviously entropy is higher in second string.
All those examples show, however, that laws of information entropy (as well as thermodynamic entropy) don't really have much to do with evolution.
There isn't going to be a logical or semantic trick to "disprove" evolution either, as it's not a suggested mathematical theorem: it's not in the a-priori space. It's an enumeration that flows from evidence. No one is claiming that evolution is a logical necessity: it's merely a theory (just like gravity is merely a theory) that is the best one supported by evidence.
How would one disprove evolution? To quote an evolutionary biologist, find something along the lines of rabbits in the Pleistocene. Until that is found, evolution through natural selection is what best fits the evidence.
What creationists are trying to get at when they make claims like "mutations never add information" would, I think, be better expressed by globally replacing "information" with something like "usefulness". Of course their claims are still wrong when you make that change (mutations usually don't add usefulness, but occasionally they do, and natural selection filters that to produce a steady increase in usefulness), and often the use of pseudo-information-theoretical arguments is just flimflam, but the Instant Refutation of saying "mutations almost always add information" or "duplications almost always add information" or whatever doesn't really engage with what the more honest ones are trying to say.