Thanks.

Update for the record (in case it may help someone): since jDownloader required Java 6, it installed it and now WireShare shows it is using it instead of Java 7 (even though the 32-bit mode is NOT selected in the Finder - Get Info). Amazing. It seems that there was something weird with my previous Java configuration in the Mac mini and the replacements indicated in my message above fixed it.

Additionally, the bootstrap file is no longer in:
/Applications/WireShare.app/Contents/Resources/Java/lib
which is OK.

And the Info.plist shows
<key>JVMVersion</key>
<string>1.6+</string>

On the other hand, the firewalls are open for WireShare:

Apple - System Preferences - Security & Privacy - Firewall - Firewall Options (Two Java lines ALLOW)
Little Snitch - WireShare ALLOW is java.org.limewire.ui.swing.Main

I have also opened LimeWire Pirate Edition (LPE) 5.6.2 just for curiosity (firewalls are also open for it). It always uses Java 6, but never connects in 32- or 64-bit mode. When 32-bit mode is NOT selected, it shows:
You are offline - Please check your internet connection.
and keeps Connecting for ever. If 32-bit mode is selected, then just shows Connecting for ever. In any case, the pesky window does not show. Anyway, since WireShare is in fact the LPE update, that does not worry me at all.

Thanks again for this great site!