A few thoughts. Nearly all NLE’s have decent proxy modes for editing these days. This involves transcoding full res media in to lighter eight proxies. Resolve does this.
A quick and fast NLE that works well with DaVinci Resolve is FCPX. You don’t use an EDL, but rather an FCPXML. It can be as basic as you want it to be.
You can also send EDLs or XMLs from Premiere, and AAFs from Avid to Resolve. Resolve works with a lot of different interchange formats, and Premiere and Avid both have Proxy editing.