Don't worry too much, the fear makes it harder to ski, much better to relax into it :)
My top would be to get an instructor for at least the first morning and ideally the first two mornings or even all week, that way you can warm up the ski legs and the instructor will only take you on what you can cope with. Then you can revisit those slopes on your own with the confidence you have already completed them.
A blue run will never turn into a black or a red, but as others have said the grading is a bit arbitrary anyway, notably between countries but also between resorts within a country. It's also super dependent on snow conditions (chopped up bumps or ice will make it a bit harder) and how busy the piste is, more people obviously reduces your freedom to pick your line. Try and focus on what the slope looks like, sometimes a quiet red with good snow will be a much easier experience than a busy and narrow blue which has got icy in places. Almost universally, very tricky pistes (steep or big moguls) will have warning banners, you will never end up on something like this by accident.
Would be a good idea to get an instructor to refresh the side slip technique with you, this can be used on any piste any time you don't like the look of something and will give you so much confidence that you can get down in places where you don't feel comfortable turning. I have been skiing for 30 years and I still use side slip from time to time, it's the get out of jail card. Also teaches good edge control :)
Lastly enjoy it! Ski what you feel comfortable skiing, take on manageable challenges to build confidence (maybe a piste with a short pitch that is steeper) and don't forget to enjoy all the other lovely things like hot chocolate stops and mountain food :)