I would combine the sentences saying, “During World War II, many men were drafted, others volunteering to serve.” In these sentences above (1 and 2), a term presented at the end of a sentence is awkwardly repeated immediately at the beginning of the following one. To avoid this unnecessary repetition, convert the second sentence into a subordinate clause of the first sentence by substituting the period after the first sentence with a comma and putting in During at the first part of the first sentence.
