BIZARRE SPECULATION TIME: So as you may know, Zelda and Samus are characters that both had transformations in Brawl (Sheik and Zero Suit Samus, respectively). However, due to 3DS restraints, they were separated. Sheik and ZSS both have moves that are resembling of Snakes.
Sheik now has a grenade attached to a string for her side B--her side B was somewhat pointless before, but now it has a small explosive punch to it.
Zero Suit Samus, being an individual character, now has a new Final smash in which she overlooks the battlefield and shoots lasers at the remaining players with a target, similar to Snake's final smash in Brawl.
Now I'm hoping these are more inspired from Snake rather than recycled. It could be argued that his absence allowed these to be used without seeming redundant OR perhaps they used him as just an influence like I said. Thoughts?
(WARNING: Very long analysis)
While Zero Suit Samus's final smash is very similar to Snake's, the only similarity between Snake's grenade and Sheik's burst grenade is that they are both grenades. The grenades function completely differently, so it's even hard to tell if Snake's grenade influenced creating Sheik's grenade.
My theory about why Sheik's side b changed is because of hardware restraints. If you take a look at the 3ds version, Link's hookshot physics were removed with Link's hookshot staying straight in the air like in the N64 version. But on the Wii U version, Link's hookshot hits the ground realistically with hookshot physics like in Melee and Brawl.
When you look at Sheik's whip from Melee and Brawl, it uses similar physics to Link's hookshot. Maybe Sheik's whip physics are too much for the 3DS to handle, and swinging around a stiff whip that doesn't react to physics would just look strange. So they decided to go for the burst grenade instead.
You might be thinking, "The burst grenade is on a string, it still reacts to physics!" well, technically it still does react to physics, but the string always stays completely straight and doesn't react realistically to surfaces. The developers got away with doing this because the string is so small, it's barely noticeable. But if you take a look at the burst grenade when it goes off a ledge, you can see that the string actually clips threw the ground! This is also why Ness's yoyo doesn't slide on the ground when you charge your Smash attack, the string on his yoyo no longer has string physics like in Melee and Brawl.
The reason why they couldn't give the strings realistic physics in the Wii U version is because of consistency. If the strings functioned differently in both versions, it would no longer make the balancing between the two versions exactly the same. The reason they could get away with doing this with Link's hookshot is because the hitbox of the hookshot couldn't grapple anyone once it hit the ground, so they just made it so when the hookshot meets it's maximum length in the 3DS version, they just stopped the hitbox. This is more evident when you hookshot in the air. If you remember in Melee and Brawl, if you hookshot in the air, the hookshot would react to physics and you could use the hookshot to hit people as it falls down. But in Wii U/3DS, the hookshot just stays in a line in the air so the hitboxes on both versions would be the same.
EDIT: The 3DS version also has pre-recorded cape, hair and cloth physics, which is why some character's clothes or hair don't react when falling or in windy stages.
EDIT 2: The 3DS version seems to be able to handle dynamic physics, as long as the model is very basic as evident by Trophy Rush and Target Blast. The objects that have dynamic physics are very simple shapes that do not transform like the hookshot, so simple stuff like Snake's grenades should run fine on the 3ds.
So Sheik's burst grenade most likely wasn't meant to be a replacement for Snake's grenade, but done because of technical limitations. The fact that the attack uses a grenade might be inspired by Snake, but it was most likely done to differentiate the attack more from Sheik's whip considering how different the attack is to both the whip and the grenade.