I know what you mean. The smallest bit of cut grass will get tangled in my dogs hair and if I dont catch it it becomes a compleat mess. I myself had never had to deal with stickers thou.
I wonder why you would prefer to have her shaved instead of finding a different park. One that does not have any weed and sticker patches. After the first few times of having to de tangle her after a trip to the park, I would have been out of there.
I have a grooming page on my web site that may be helpful. It may help you find an easier way to get those tangles out.
Grooming - Dawn's Yorkies Ohio