Topics in Even Haezer

Although during the actual blessings of the Aliyah, the Olah is to hold onto the right handle using his right hand and left handle using his left hand, and the Baal Korei is likewise hold onto the left handle during the reading, no preference is recorded in the Poskim regarding which hand the Baal Korei is to use to hold onto the left handle, and therefore he may choose whichever hand he wishes, although usually it is easier to use the left hand. However, in the event that the Baal Korei receives an Aliyah, then he is to only hold onto the right handle using his right hand.

Source: See Michaber 147:1; M”A 139:13; Kaf Hachaim 139:24; https://shulchanaruchharav.com/halacha/holding-onto-the-handles-of-the-sefer-torah-during-the-aliyah-why-and-how/ and https://shulchanaruchharav.com/halacha/chapter-4-the-baal-korei/ ; https://shulchanaruchharav.com/halacha/chapter-4-the-baal-korei/