How to safely kill small clumps of blackberries growing in amongst native vegetation, alongside a creek?

We live in rural Tasmania and have small clumps of blackberries growing on our property amongst native vegetation, alongside a small creek. The creek is our source of drinking water. We would like to know the best way to safely remove the blackberries without killing the native vegetation or contaminating the water source. It seems to us that the best method may be to cut the blackberries at their stem in dry weather and paint a small amount of poison/herbicide onto their stem. However, we are not sure what herbicides may be appropriate for this technique, given the environmental sensitivity of the waterside location. If you are able to recommend an appropriate product and approach, that would be much appreciated.