Both ginkgo and cork bark elm air layer well. Ginkgo is slow - an air layer will take all summer, occasionally 2 summers, but it will work.
Cork bark elm, can root very quickly, in as little as 6 weeks, or it can take longer, but much more quickly than ginkgo.
Cuttings, both will root from cuttings. Cork bark elm, even fairly large diameter cuttings will root. Most people use semi-hardwoord cuttings, usually taken in late July or early August in my area. But hardwood (later season) cuttings also work. Hardwood cuttings would also be your larger diameter cuttings. I would take these in September. Keep them over the winter the same way you would winter an adult cork bark elm tree with roots.
Ginkgo from cuttings is tricky. I have failed every time I tried. But I have heard it can be done. The ones who had success took the cuttings in late autumn, after the leaves have dropped. Then planted them, and kept them cool, bright, above freezing but below normal household temperatures. I believe in the 40's for the winter. You will need to explore the posts here by others, and maybe check out Dirr, his book is in many public libraries. "Propagation of Woody Trees and Shrubs' by Michael Dirr. It is an old book, through many editions and printings. Mine is the 2008 6th edition, but I can not find it right now. Lost somewhere in my office.