I use that same strategy in Wordle. Most often my first word is SOARE and the second is MINTY… unless I got like three matches in the first word, it’s better to get extra data quickly.
That's a best case of 2 additional guesses and worst case of 3 (expectation of 2 1/3) which is better than your strategy, which has a best case of 1, worst case 6, expectation 3 1/2.