In theory, anything is "possible". But recombination within a single "species" (nobody has a solid definition for what the terms genus or species should be based on in viruses) are very common in many types of viruses, and essentially never observed between viruses of different "species", let alone between different classes such as single-stranded and double-stranded DNA viruses. For one example, most of the Sarbecoviruses (such as SARS-CoV-1 and SARs_CoV-2) show evidence of historical recombination with other Sarbecoviruses, but there is not yet any description of a Sarbecovirus recombination with any of the other betacoronaviruses (Merbecoviruses etc) let alone with alpha or delta coronaviruses.

There is evidence that protein coat swapping has occurred historically, even between DNA and RNA viruses. Still these events tend to be rare.