ZIP traditionally encodes file names using the IBM437 encoding. However, as far as I know, many tools (incorrectly) tend to use the default encoding in the system, which is likely to cause problems in this situation, since both ends can use different encodings.
In theory, ZIP also supports UTF-8 by now, which should solve these problems, but again, tool support will be a problem. For example, as far as I know, Windows Explorer ZIP archive support will not be able to process UTF-8 encoded file names.
So, we are done with this: both ends must agree with the encoding used for the file names, and you will need an encoding that supports all the characters you have (any Unicode encoding will be fine, I'm not sure about IBM437, though). ZIP has come a long way, and therefore there are many tools that generally disagree with the encoding. If possible, explicitly specify the encoding to use and prefer Unicode. In terms of compatibility with arbitrary tools, you might be better off using a newer format designed with Unicode in mind.
7-Zip supports it starting with version 4.58 beta, according to the change log, but will only use it if the local code page does not support the required characters. Using the command line switch -mcu will use UTF-8 for anything but ASCII. Local encodings usually only differ in a range of characters other than ASCII, so this is likely to do the trick. That is, if the tool used for unpacking also supports UTF-8 (which is most likely for 7-ZIP than for ZIP, because it is not as outdated as ZIP, and there are fewer tools for unpacking).
WinRAR may also be worth a try.
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