I am not sure I understand the precise idea of your description, but here is one approach...
A few things to note about the video demo just below that is at variance with your request:
1) The entirety of the transition images get blurred, not just the edges.
2) It is occurring faster than You are probably envisioning.
3) The example is actually a complete scene change.
However, the same principles would apply to your request - just adapt to your own variation.
I would create the initial effect in a video editor - then maybe You are done - as You are going to embed it anyway.
BUT do consider the practice and experience You would gain by also experimenting in Hype - which might bear fruit at some future time. The process would be to export the frames from your video editor as PNG or JPEG files and then selectively use "keyframe" images (You won't need that many) needed for the effect - along with the judicious use of fade-in, fade-out in the Hype timeline itself.
The video effect:
Breaking down the key changes to the frames:
The image does a simultaneous lateral movement & blurring. The blurring ramps up during the transition.
Do note that the blurring is directional - lateral to match the movement.
The next scene moving in with an identical (or near identical) blur setting and movement.
The blurring effect is at a maximum.
Just about there - the blurring is significantly lessening as the new scene slides into place.