One thing I've never gotten about the 1995 flashbacks.
Jackie has just become Boss, not long before. Junior is angry and feels he should be Boss and is creating a very tense situation by testing Jackie's authority by hijacking his truck. He's sending a very clear "Fuck you" to the new Boss. This has the potential for war. Afterwards, Junior lams it down in Boca.

Tony sends Pussy down to Boca to pacify Junior and get him to agree to a sitdown. Pussy says Junior was nervous the whole time that Puss had been sent to pop him.

My question is, wouldn't it have been easier and made more sense if Tony had been sent himself? He'd have Junior's trust and be able to coax Junior to settle this shit a lot easier than one of Tony's buttons. I don't think Junior would've suspected Tony was there to pop him, anyway.

So why send Puss and put him in charge of arranging the sitdown?

IMO tony did't have that good relationship with junior that time (you can even see in season 1 that they cannot settle a small beef between their crew's).
but why sending pussy ? i have no idea, you right its really seems weird.

But remember, in Season 1, Jackie is dying. There's no real leader keeping the two of them in line. Whereas in '95, Jackie was healthy, had the backing of the Family, and would not hestitate to kill Junior if Tony couldn't get him under control. Junior would've understood this, and much quicker if it was Tony coming down and saying "Look, Uncle Jun...You gotta settle this shit with Jackie. You wanna wind up popped?"

Pussy and Junior had no relationship, no history, Pussy was one of Johnny's guys - why the fuck should he trust Pussy to arrange a sitdown? How does he know Puss isn't setting this sitdown up for Junior to be popped?

He's meant to be marginally older than Tony in the show. He was initially with Johnny as you said. I feel this is why he is sent.
It was my understanding that Johnny and Junior worked together when possible although they ran separate crews. My assumption was that most of Johhny's guys were okay with Junior and his guys and vice versa of Junior's crew w/ Johnny. I would imagine there were a few guys in each crew generally disliked, but as far as in family cooperation, you can safely assume that Johnny and Junior told their guys avoid issues with each other.

Pussy seemed to earn well while being a generally well liked and well included person. He was friendly with Johnny Sac while never rising above the rank of solider. To be that trusted by Tony, one would imagine he was well liked by Johnny as well especially after the 'Unrest of '83". This is what leads me to believe that Junior would sooner see Pussy as a neutral messenger than see Tony that way.

Another easier answer is that Tony stayed in Jersey for his own safety, why go risk getting shot at by Junior's bodyguards if he didn't really have to? If you were Jackie and were about to bump Tony up, why send him when you can send a career soldier like Pussy just in case another goes wrong.

yeah all day i agree, its seems like pussy is a good earner and funny guy who almost everyone liked so its kinda make sense(not 100 %) that he would be sent to a meeting with junior.

He also got arrested in Boca. It makes you wonder if Pussy volunteered to go down there with a hidden agenda.