It does essentially nothing for recovery besides stall. It has absolutely ZERO effect on horizontal momentum. It isn't useful for stopping vertical momentum either since jumping is more effective for downward momentum, and for dying off the top it actually launches you upwards instead of stopping you if used immediately after the hitstun ends. Once you're 2 frames beyond when the hit stun would normally end you won't die by passing through the blast zone either. In the event you skim just along the top blastline, if you were to double jump or shine on the 1st or 2nd actionable frame after the stun you would actually die whereas you wouldn't had you done nothing at all.
Double jumping has an instantaneous effect on your horizontal momentum, so when dealing with the side blastline, DJing immediately will allow you to survive a few percent higher than shining/shine DJing/air control would.
Regarding the boost you get by using shine at the end of hit stun, it gives you a vertical boost proportional to the amount of your original vertical knockback (DI included, so you'll get more of a boost off say Marth's f-smash by DIing up/towards than no DI at the same %). It also carries over into your jump if you DJ. The thing is though, you also get it by DJing, up b-ing, forward b-ing, or airdodging anyway (may be different for other chars), and since the shine does nothing for your horizontal momentum you still drift away and lose enough horizontal distance to negate the extra vertical distance you may get with it because of his fall speed.
In the end, immediately DJing/full shine->DJ/shine->immediate JC all work out to pretty much the exact same recovery distance, though shining will get you killed if you barely recover from stun the moment before reaching the side blast line as opposed to DJing. It will also take slightly longer to make it back if you add a shine in too obviously.