At 5.1m long it may prove too large (length wise) for the Harrier II.
Pretty sure that the RAF had assessed Storm Shadow as being a feasible option for Harrier GR.9, and SCALP/Storm Shadow is also 5.1m in length.
However, I believe there were concerns with the bring-back weight when carrying Storm Shadow at sea (which was kind of the point of integrating it on Harrier), so the MoD revised down the requirement to just Tornado and Typhoon, and it never materialised after that - with the missile later being used as part of the justification for keeping Tornado instead of Harrier.
I imagine all that would largely hold true for KEPD 350 as well.