The Daimyos and even the Tokugawa Shogunate Gov't would never allow Japan to become a 'protectorate' to any foreign nation ...
WHat they would allow is of little importence. If they can't defend themselves, even if they want really hard to not be "protected", they would be nevertheless.
Japan had fought off the Mongol Invasions at least twice...
The first invasion failed because chinese and koreans part of the invading army were revolting themselves.
The second invasion have both is exploring raids defeated and his fleet destroyed by a tempest.
Their National Identity as one Nation as strong as ever would likely demand that they combined their forces as a single entity.
It's quite surprising then, that Japan relained divided following clanic structures. Seriously, talking of "nation" for middle-ages' Japan is what is more close of an historic blasphemy.
But even regardless of that, many states with a strong identity have been colonized too in Africa and in Americas, Japan wouldn't have been an exception because they were lucky enough that the Mongols didn't managed to make a proper expedition.
However weak Japan was during the 1850s and 1860s in comparison to 1860s Imperial Russia under the Tsars...
But ...
Japan wasn't weak : it was doomed. US forced the opening to allow themselves some harbours if they want to protect future interests. If Perry don't manage to do that, Russia is the obvious choice : others european imperialism are busy elsewhere, quite far (Latin America, Africa, Middle-East).
In fact, UK and France could see the Russians busy in Japan instead of Eastern Europe a good thing.
They might garner some 'allies' from either Portugal or England to counteract any attempts by Tsar Russia to make the Four Isles of Japan into a protectorate of The Russian Empire...
WHY? Seriously, WHY?
England was too much preoccupied by Russia in Middle-East and Eastern Europe to not be happy to see the Tsar having fun with Nippon instead of Pan-Slavic gibberish or Central Asia.
Hell, they would probably congratulate them for that.
Portugal? No. One thousand times no. One billion times NO. A google times NEIN.