A non-breaking hyphen is what you want. If it's not supported by the default reader font, that's not your problem (besides, the rendering software should be smart enough to use a normal hyphen if the specific character is not found). But actually, is it so grave if the word is split at line end? That's probably better than the additional word space that would result if the whole bit is moved to the next line.
You could also try a non-breaking zero-width space (word joiner), & #8288;, after each hyphen, but you'll probably be in the same situation if the font has no definition for it.
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