Final answer:
William Howard Taft was the American president who advocated for 'Dollar Diplomacy', substituting dollars for bullets to exert American influence globally, leveraging economic power rather than military force.
Step-by-step explanation:
The American president who argued that the United States should "substitute dollars for bullets" when it came to wielding American influence around the globe was William Howard Taft. This approach was termed as 'Dollar Diplomacy', which was a significant shift from the earlier strategies of using military strength and coercion. Taft's policy relied on using American economic power as leverage to secure markets and opportunities for American businesses, though he resorted to military intervention when economic coercion was not sufficient. This strategic foreign policy aimed at ensuring that the US could maintain its status as a world power without the excessive use of military force.