The USG does not typically respect other countries' sovereignty where doing so would diminish its own.
That's pretty much the definition of sovereignty.
Just as importantly, many of your prospective customers will worry that your exchange may go offline, which may send them elsewhere.
It's the first time I hear such a concern...
If you still prefer the marketability of .com, there is a workaround you may favor: for anyone going to jp.peatio.com, immediately redirect them to a true .jp domain or preferably to an offshore top-level domain you can trust ("jp.peatio.ok"), and so on for the other countries.
The redirections must be visible so that your customers will always know the true URL, so that when your .com is pulled, they know what to do.
The redirections should properly support https:// or they will encourage man-in-the-middle attacks. (For that matter, anyone going to the http:// version of any of your sites should simply be told to try again with https://. It is always insecure to passively redirect non-SSL to SSL connections. Most sites violate this critical rule.)
That would look dodgy as fuck and be counterproductive as hell.