I think that is very likely that he will give it to navani but I don't know if they will be able to do this secretly because everyone knows the "sick for a week" play already because dalinar flat out told people that. also if navani does pester dalinar to give it to her it won't be because she thinks of it as a fabrial because she will undoubtedly ask one of the radiants about it and find out that the blades are really spren. If she asks kaladin she will find out that the honor blades are not spren and were created afterwards to emulate what the spren were doing.