The first option is correct. There is a general rule that you should make a page break at an existing hyphen and hyphens always appear at the end of the first line rather than at the beginning of the second. See, for example, Rule 2 at this link http://englishplus.com/grammar/00000129.htm
Note also examples in a previous post at this forum: What are the rules for splitting words at the end of a line?
Often, in manga translations, confusion between Shu-chan and Shuchan is avoided by having a short summary of the relevant honorifics and their rough English equivalents, distinguishing, for example between Shu-kun and Shu-chan such as the one found at http://tvtropes.org/pmwiki/pmwiki.php/UsefulNotes/JapaneseHonorifics
but simpler.
In particular, it is also common to indicate the fair strong meaning involved in omitting any honorific (i.e. the "null honorific").
Also, as in almost all cases of hyphenated words there is a constant tension between a trend towards segregation and stating the suffix as simply a separate word (suffixes for which this is sometimes or often done are noted in the TV tropes link above) and merging the two into an unhyphenated single word (I haven't seen this in manga translations).
(FWIW, a similar honorific explanation is appropriate in any case where Arabic names are present as honorifics are omnipresent there as well, although with very different meanings).
Another way to avoid ambiguity that is fairly common in manga translations is to carefully avoid line breaks in sidebar text about characters that break the third wall and provide character profiles for readers (e.g. favorite food; blood type; height; weight, etc.), or in the intro recap/preview that is found at the beginning of many manga volumes and mentions the main characters by name, or in back cover material.