The shogunate had already embarked on a modernisation programme and would have continued pushing it.
The shogunate would have collaborated with the imperial house and eventually paved the way towards a constitutional monarchy with the Tokugawa retainers and not the Satsuma-Choshu clique, running the show.
Japan would have collaborated with the European powers and the US. The shogunate had good relations with France, so perhaps the French would have remained their closest ally for a while.
If the Tokugawa had been able to keep the radical military elements in check, likely, Japan would not have entered WWII or would have sided with the Western allies. (This begs the fascinating question of what impact that would have had on China and the Communist insurrection there.)
Had that hypothetical Tokugawa government not succeeded in stemming the rise of militarism, history would not have been so different, I assume.