The situation is not so simple. Let's assume that you want to study the naked CDs. In solution NMR usually you can study the non-exchangeable protons only. In many cases it is enough.
If you are making the xSY experiments in D2O usually you cannot do anything with the H-bonds because they are not really existing. Perhaps in H2O doped with D2O you can get something, but it depends on your instrument - you need to ask some NMR experts..
Using DMSO the problem is a little different, because the DMSO can form complexes with CDs (and the slow D-H exchange can also affects the results, particularly upon long experimental time). The (competitive) complexation with DMF has considerably smaller effect.
Other (deuterated) organic solvents are not really solubilize CD/CD-complexes, they may also have competitive complexation, or they can even destroy the complexes (mixture of EtOD/D2O, for example).
Diffusion experiments might help because in a well-designed experiment you can get information on the complexation/dissociation speed, too.