Clone, Design, Build, & Launch.
Many may not be aware of it, but you can ask Wild Apricot support to clone an existing site and thus you are able to perform all design and customization on the clone and not effect your live site. That is what we did for our latest custom design on http://www.naro-us.org/
We requested their live site be cloned for us. Then we built the custom design on to the cloned site. Performed required revisions and cross-browser optimization. Once client signed off, we migrated design to the live site in under 45 minutes.
So, the challenge of design and development on a live Wild Apricot site is under control.