In the first instance, "Dutch aunt" would draw so much attention to itself that you could only use it in a somewhat wry, playful way (which would be effective, in my opinion). If you don't intend this, it would be better to avoid the expression altogether.
"Doubting Thomas" is so well-established that it might fare a little better, but the gender difference would still jar a bit. You could soften this by saying, "like a doubting Thomas" instead of "is a doubting Thomas." Again, "doubting Thomasina" would get the message across, but humorously.
[native speaker & writer, not a teacher]