While I don't have a sensory avoider I know of some kids who are and seeing I haven't confined this to any sort of therapy but just in general therapy type things or solutions for tapped out moms. As I come across ideas for avoiders I try to post them although they may be something that won't fill my son's particular needs.
One thing that can get very messy... and sticky is glue. Sometimes doing artwork for these kids is just too much because of all the sticky things that are involved. So if you should happen to try to do a craft that is going to involve glue of some sort you can replace the glue with clear contact paper. The kids place the contact paper on the table and put what they want glued down on the contact paper and it sticks. Then take another piece of contact paper and place over. If you didn't line it up correctly then you can cut around the edges to make sure there is no sticky surface.
Of course, some kids will avoid the sticky feeling all together and in that case rather than having them put the items on the contact paper. Give them a regular piece of paper and put their design on the regular sheet of paper and then cover that paper with contact paper for no mess or sticky sensation!