You can safely take that Ginko limb without issue, Ginko's generally are pest and disease resistant. It's important to take care and make a good pruning cut. This limb, for example, you don't want to take all at once with one cut. One weight reduction cut, with a final cut just outside the branch collar. For even heavier wood, a 3 cut system is often utilized, beginning with an undercut halfway up, then an overcut an inch or two offset, further from the trunk, causing the branch to cleanly snap and fall. This is a bit overkill for what you're doing, but you could implement it. 

For explaining pruning cuts, pictures and diagrams are most helpful, I've found this guide by the University of North Dakota which you could refer not only to for proper pruning cuts, but also where to prune to develop a good structure, if you ever intend to that in the future: https://www.ag.ndsu.edu/carringtonrec/archive/northern-hardy-fruit-evaluation-project/fruit-project-results/basic-pruning-cuts

This crab apple is very gnarly - I see only water sprouts. If more than a quarter of the canopy of the tree is water sprouts, then I would suggest not doing it all at once, but a remediation project over several growing seasons. It's safe to remove about a quarter of the tree's canopy, but that should be about it for the season, otherwise you risk sending the tree into shock. The big disease with apples, is scab, which pruning only helps alleviate. So by pruning, you're if anything, increasing its resistance to scab by creating better air flow and light penetration. However, if you're serious about improving this tree, you may want to preventatively treat it for scab, as it must be preventative, and there is always disease pressure, which can make a healthy apple tree look almost dead by August, regardless of how well you prune it. 

Best of luck.