With the recent Cwicly updates, the html tag for a block is shown consistently in the top right of the block inspector and you can update it by typing or selecting from a dropdown.
When you add an active link to a block, this tag shows only two options (a and button), and you can no longer edit the tag for the block.
In this case, all you need to do is open the link dialog and temporarily deactivate the link.
You can then edit the html tag for the block again and reactivate the link.
All of your link settings are remembered, so it is a quick process.
This is particularly useful for headings as it is common to want to change the heading level (e.g. h1, h2, h3, etc).
Hopefully this saves you some valuable time.