Some shops will offer 'commission sales', where they will add on a percentage, but you have entrust your instrument to them to look after. Unless it's a trusted specialist, not sure that it's viable these days.
As has been said, part-ex prices are often insulting, in order for the shop to make it worth their while. Not viable.
Private sales, either here, the Bay of E, Gumtree, Reverb, or some other site would be the way to go, but needs a lot of trust, and careful packaging if you're going to post.
Thankfully, the marketplace on BC is great.