As long as the binary is under an open source license, you would have rights to disassemble it and distribute the results (optionally modified). However, with a permissive license like BSD or MIT/X11, people who use your work have no obligation to license their modifications under that same license.
With a copyleft license like the GPL, people can distribute their changes only under the GPL as well, and they must provide their full corresponding source code (or else you can take legal action against then, or at least credibly threaten to do so). However, this is quite a bit more than you want!
A middle ground might be the Creative Commons Attribution-ShareAlike (CC BY-SA) license, which requires that modified binaries must be distributed under the same license, but not necessarily be accompanied by corresponding source. That way you can be sure that you have full rights over the binary you receive, and others don't have to worry about distributing their source code if they don't want. CC BY-SA also means downstream redistributors can't monopolize their copy -- all recipients have the same redistribution and modification rights as the person they got it from.
Note that someone might carelessly or maliciously say, "I didn't say you could use my modifications! Stop or I'll sue you." In that case, you can answer back, "I said you could redistribute the contents of my original binary only if you shared modified forms freely. If you aren't interested in doing so, I can sue you right back." It sounds like community norms will prevent matters from getting to such a point in the first place, but this is the legal safety net CC BY-SA provides.