'Would more likely result in such a condition' Except that no? That's not how incest related issues work.
What do you mean no? Inbreeding means closely similar alleles in the genes would be combined, meaning more likely occurence of previously only genetic carrier issues. We see this with examples like Habsburg jaws, European royalties hemophilia issue (from Queen Victoria being a carrier), and all the various health issues found with ancient Egyptian pharaohs. Sure impregnation process is genetic lottery, but inbreeding means the gene pool is narrower and thus genetic defects in the bloodline have more chance to come out in the resulting kids.
If you're saying incest won't cause a kid to be born without a hand, well, currently the consensus on symbrachydactyly is that it's not caused by genetic reason whatsoever (and in fact no one knows yet what causes it), so in that case you would be correct. But incest causing a genetic defect to occur in an offspring isn't such a weird thing, though most of the time it takes repeated incest, but well, genetic lottery being genetic lottery. So not born with a hand being Katabuchi family's inherent genetic defect isn't such a wild plot point imo.