The 1841 British edition replaced the present perfect have had with the simple present-tense have (by omitting the had ). Either reading is theoretically possible here. For another example where the 1841 edition accidentally omitted the perfect, see under Mosiah 23:31. The critical text will follow the earliest textual sources in maintaining the perfect in Alma 19:9.
Summary: Maintain in Alma 19:9 the use of the present perfect in “I have had no witness”.