Hi, C. If you're looking for a totally safe stripper under all conditions, you may as well just replace the moldings. However, there are several relatively safe strippers. Personally, I like and use Citristrip. It can give a mild chemical burn, and you should have good ventilation, but other that that, it is pretty safe to use. The one that you think is applied like wallpaper is probably Peel Away. This is a lye based paste in it's most common variation. You put it on with a spachela, put their special paper over the top, then remove the paper and most of the lye and paint then remove the remainder by scraping it off. You then neutralize by washing with white vinegar and rinsing.
Since you will be leaving these products on for some time, you will need to keep kids and pets out of the area while the products are exposed. You will need to wear rubber gloves and eye protection while working with them. Because they are not as quick working as the major stripper product, you may have to let them work for 24-48 hours, depending on what they have to remove. The most common stripper products are methyl chloride based and I feel that these are unsafe to use outside of a closely controlled industrial environment. You will want to leave a window open slightly with Citristrip but the Peel Away basically does not have fumes.
Both the products that I mentioned by name have web sites. You might check for further info there. But I will say that with proper care and consideration, you can safely strip your moldings.