Az, if you take, say, three pairs of shorts/tights, so you can rotate among them and let damp ones dry, you should be fine. We started cycling in the rain here in the PNW around 2003, with rainpants, and dropped them totally within the year. Last use was our trip to Iceland, where everybody walks around in rainpants for very good reasons.
Cycling tights are meant to absorb AND dry reasonably well. I think you'll be more comfortable and do just fine without rainpants.
"My predominant feeling is one of gratitude. I have loved and been loved;I have been given much and I have given something in return...Above all, I have been a sentient being, a thinking animal, on this beautiful planet, and that in itself has been an enormous privilege and an adventure." O. Sacks