I'm looking for a similar markdown syntax to ­ in HTML.
I know there are hard breaks in markdown, but I'm looking for something that acts like ­ or similar.
Most Markdown processors can process any HTML entity, including ­. So you can use that.
An alternative is to insert the SOFT HYPHEN (U+00AD) Unicode character directly. However, the feasibility of this depends on how easy your OS and/or editor makes entering arbitrary Unicode characters.