I feel like the question is a little loaded, but I gather you're wondering whether Elizabeth I was actually weak/feeble relative to other women of her time? She lived until she was 69 (life expectancy in 17th century was probably just a little lower than this at 50-60) and was in good health until a year before her death, so no, she was probably referring to the archetypal view of women rather than herself specifically.

But referencing a gender-based, cultural concept doesn't necessarily equate to "playing to the troops' misogyny" :P This is actually a perfect example of why "misogyny" isn't a black-and-white concept, especially throughout history.

Remember that women living in less egalitarian times didn't think "Gee, I wish I had equal rights to men! I'm a fully realised 21st century feminist on the inside, but I have to keep it to myself and/or be really subtle because of my place in time & history!". Many women, many strong and influential women, who have lived throughout history probably would've taken pride in, and dealt with complex emotions surrounding virtues that modern women would consider demeaning and sexist.