Also, to support your claim, one would need evidence that the child mortality of the past reflected genetic unfitness (as opposed to poverty or the unavailability of antibiotics).
In any case, we have to go back to the question that the GP asked, that dogs are malleable doesn't help us. Does reduced child mortality really cause more mutations to accumulate?
However, dog breeds are not species and, given their non-random mating, don't really tell us much about whether 200 years is long in vertebrate evolutionary time.
As far as humans go, I will grant that allele frequencies may have changed if you pick an isolated subpopulation of humans (say, everyone in Greenland) but even that seems extremely unlikely.
As an aside, there are researchers who are using the caste system in India as a way to explore genetic architectures within a civilization. As these castes have existed for considerably longer than the period we're discussing, meaningful allele frequency changes may arise.
http://wasdarwinwrong.com/korthof97.htm
I would guess it is wrong; we are on a track where genetic manipulation to treat blatant defects will (relatively shortly) be cheaper than the traditional medical treatments.
Parents could choose to have children created from their healthiest genes, rather than leaving children to be shotgunned with a random and increasing fraction of damaged genes. Genetic repair would replace the ancient cruelty of natural selection, which only fights entropy by tormenting organisms because of their genes.
The concern espoused above is that we won't be able to fix the problem.
Now that's a limited view of the process that created life. Natural evolution also pays back by upgrading the gene pool.