I use wood glue (It is white in the bottle but after it is dry it gets transparent) That glue didn´t make those filaments.
For small parts i make a blob on a paper at take a pin or something like that for getting it on the part i will glue.
Thank you guys for your input, but I was asking starbuck in order to understand why the glue gets on his parts and to give him some advice on avoiding that.For me, I use this one. The excess of glue disappear when it dries and there is no changing on the colors. The paper does not soak it too much so I never have waves in my paper joints. Plus, it dries faster than wood or white glue.