As you're a woodworker, you can probably make a handsome box for chisels with ease - perhaps one as handsome as Derek's drawers! (Them wooden ones, not his under-strides). But when such a box is large (for the chisel range expansion purposes) or you have numerous of them, they become rather less "portable". In what way do you want the chisel-clasper(s) to be portable, by the way?
Personally I have a lot of such tools wrapped in leather tool rolls made by my wife, who is adept at the making of all sorts of sewed-up stuff. She also makes leather covers of various shapes and fastenings for the sharp parts of tools - chisel ends, knife blades, axe/adze edges and so forth. The advantage of home-made rolls (and boxes too) is that you can size the pockets or other tool restraints to suit the handle sizes, tool lengths and even the blade shape. A lot of commercially sold tool rolls are nae gud for certain tool marques, with Ashley Iles larger gouges and chisels having handles too fat to get into a lot of tool pockets, for example.
Leather and cloth can be a medium for condensation and thus for rust to form on any wrapped-up steel - but only if the surrounding atmosphere is going to impart such condensation. Such as atmosphere is going to rust carbon steels anyway, in a leather tool roll or not. The added risk is that you don't notice when they're in a roll or box, unused for significant periods. Best to keep tools out of damp places, if possible. Or put everything (tools and rolls and boxes) into cupboards with effective moisture absorbers/rust preventers in them.
In the workshop (i.e. not ported about the house or to remote jobs) magnetic rails are very useful, as every tool and its shape/type can be easily seen, reached for and replaced. This keeps the bench top clear. You'd also notice any rust, toot-sweet.
One syndrome with many of us tool-wielding types is the cluttered bench, with a dozen or more tools used and put down to eventually build a tool-tangle. This can damage edges, as they dunsh each other during your digging for a tool at the bottom of the tangle. Also, you may withdraw your paw to discover blud! Magnetic tool rails help keep the tools off the bench. Or an organiser like the Beavecraft frame-with-holes can be made to keep the working tools on the bench but tidily and visibly.
https://www.cyclaireshop.co.uk/beavercraft-wood-carving-knife-tool-holder?search=Beavercraft&page=2
You can make it to a size and hole-shape/number to suit your particular tools.