Should Yoshi have another game of his own?

The shoal.

His fish hold the weapons.

The Shoal
From The TimeSplitters Wiki
The Shoal

Unlocked by Default
Species Fish
Size Normal
Accuracy N/A
Agility 5
Stamina 5
Fire Proof 5
Shock Proof 2
Default AI 4
Native TimeZone Unknown
First Appearance TSFP
Relations N/A
Games TSFP
TS1 Gesture None TSFP Gesture "It's time you slept with the fishes"
TS2 Gallery None TSFP Gallery Eat krill...eat krill... eat krill...

The Shoal is, as his name implies, a shoal of fish, gathered around a large whale which acts as the character's 'head'. He sports a black top hat and smokes a gentleman's pipe, and instead of arms, he carries and fires weapons using the multiple smaller fish that are gathered around him. The shoal is one of the few floating characters.

TS1 Gesture N/A TSFP Gesture Hops down and does a flip while making multiple monkey noises.
TS2 Gallery It's a monkey. TSFP Gallery Yep, it's still a monkey.

The Monkey has been a recurring character in the TS series. Free Radical Design has been said to have a fetish with this character.

1920 Aztec Ruins
The Monkey is encountered in this mission as an enemy that stands still and throws explosive melons. Their small size can make them difficult to spot, and their melons do considerable damage which can make them a dangerous foe.

1969 The Russian Connection
In TimeSplitters Future Perfect, a Monkey appears in a cell as one of Khallos's hostages on 1 player only.

Monkeys with guns...

Yep

Mr. Socky

Unlocked by TSFP: Unlocked by beating Arcade

League match "Sock It To Them"

Species Puppet
Size Large
Accuracy N/A
Agility 5
Stamina 5
Fire Proof 2
Shock Proof 8
Default AI 3
Native TimeZone Unknown
First Appearance TSFP Arcade Mode
Relations None
Games TSFP
Mr. Socky appears in TimeSplitters Future Perfect as an unlockable character. The character appears as a giant sock with two fingers for legs. It's hands are sock puppets. Mr. Socky is unlocked by beating the league match: "Sock It To Them", in which you play as Mr. Socky.

TS1 Gesture None TSFP Gesture Flex's while saying "My friends call me spoony legs"
TS2 Gallery None TSFP Gallery Normally just an ordinary sock, when things get rough he turns into... Mr. Socky, the Psychotic Sock-Monster!

bad picture for Socky but nevermind.

Okay, we've been off-topic long enough, so...

Throughout the Yoshi game, there should be a character that constantly bothers you, similar to Koopa Jr from Paper Mario.

Yeah true

Perhaps the two pirates who follow Captain Berry Beard.

That would be good.

They could block ways or start many of the Mini Boss battles, like Kamek did in SMW2.

Yep.

Yay 😄

They would be annoying, too.

If you want an annoyance, those two would do well, and they fit with the believed main villain.

Yeah.

It's not like they are random, they play a part in the main story.

Yeah, they do.

As the cabin crew.

Yep.

Fun times 😄

They would taunt Yoshi and his friends throughout the whole game until they're defeated in battle.

Aiding the captain in his boss battle.