Is it considered that impurity has transferred to the entire body due to doubt about the continued bleeding of wounds during showering, or is merely wiping the blood and performing ghusl sufficient?

The best cure for waswas (whispers/obsessive thoughts) is to ignore them. Impurity is not transferred merely by doubt; the default state is purity, and one does not deviate from it except with certainty. Sheikh Ibn Uthaymeen (may Allah have mercy on him) said in "Fatawa Nur ala al-Darb": "Doubt does not remove certainty. And certainty is that this ground, or these furnishings, are pure. So if a person doubts whether impurity has afflicted them or not, then they do not become impure; rather, they are legally pure." This is supported by the hadith of the Prophet (peace and blessings be upon him): "He should not leave - meaning the mosque - until he hears a sound or perceives a smell."