Personally I'm not seeing the Lukan author avoiding the reference to soul in Psalms but I may be missing something.
It's about the interpretation in v. 31, not the quotation in v. 27.
ouk egkataleipseis tèn psukhèn mou eis hadèn oude dôseis ton hosion sou idein diaphthoran
oute egkataleiphthè (passive, subject "Christ" instead of psukhè) eis hadèn oute hè sarx ("flesh") autou eiden diaphthoran.
The point being, Luke-Acts tends to use psukhè a bit more strictly along the Hellenistic line (it is less influenced by the Semitic nephesh) and insists on a bodily resurrection.