Would you say he does "Better" than ICS do though? Save for the links, i had been thinking about Doc for the peach MU.
Could you show me where there is more correct info on MU for link? Cheers.
He's a fun character despite the slowness
Technically he can do better than Icies against Peach sometimes since he can fight her somewhat due to similar speed, and a good example of higher level play is with SAUS vs. Kalamazhu at GOML. Even though Link loses the set, you can get some ideas of how Link can play the MU. Yet there is also the potential to be broken down in the MU against Peach as seen with Lord HDL vs. Armada back when HDL used Link. Reptile gave some good tips as well. The other suggestions have stated what needs to be said though, Link may not be the best long-term, on-the-side secondary for you. For the fact of the matter, it takes some dedication to be good with Link in the current metagame.
Peach in the current meta is weaker to Fox and Puff, but you said that you don't want to use those characters. In this case, I'll just list the characters that you could potentially use other than the previous ones: Falco, Sheik, Falcon, Marth, and Peach (of course).
Falco can do well until the upper levels as of right now since Armada and MacD are incredible against Falco. Sheik is really at an advantage, but she's not at a disadvantage either. Much of the game is in the neutral until either character gets a punish opportunity, and Sheik is one of the easier characters to optimize your punishes (Armada wrote how Peach should play the Sheik MU, so you can look at it in order to figure out how to fight her better. It's on the Melee It On Me website). Falcon has numerous tools in the Peach MU as well although it's debatable again at the top level except it's with only Armada this time being the god. Marth is another good pick since he naturally controls the neutral better than Peach, and he can setup his kills well if you are crafty and study the character some. Just make sure to watch out for turnips since Peach can approach and punish better with them. Of course you can play the ditto as well, but there is the chance of the more experienced Peach main taking advantage of how you play their character. Also, she becomes very technical as you get to higher levels of play, so she requires dedication.
As for other characters, the established mid tiers can have a rough time with Peach, but there still is not much developed in these MUs in comparison to their Spacies MUs. Yoshi takes too much dedication to be considered for a secondary (at most, he's a dual-main as well as a main), Ganondorf has a bad MU against her as well, and not much is developed with Luigi. There has been some development with Doc, but he still has trouble at the top level. The epitome of the MU currently is Shroomed vs. Armada, such as at EVO. Mario should be similar to Doc, but he focuses more on gimps and comboing into Fsmash and Dsmash, so the MU should be worse for him considering how Peach recovers and is floaty. Knowledge of Pikachu's MU is mostly based on how Axe plays the MU, but he's not always used Pika against Peach. Besides the other mid tiers mentioned, there is Samus to use, but I don't know how that MU goes very well, so I won't try to give an opinion on something like that.
Below those mid tiers, what you've got left are of course our character, Link, and Young Link. Young Link is a common secondary that can be used against Peach (since he is used mostly as a secondary for the three main floaties: Puff, Peach, and your character Icies) if you aren't looking at top or high tiers, but it won't be easy either, just easier than Link. Some players who used him against Peach are Axe and Chudat.
Overall, if you want a quick secondary, the top and high tiers have the options. If you want to experiment with other characters, you will have to do more work and research for mid tiers, except for the Links, but even then you still have to work with the characters for a while to succeed in the MU. I personally think both Links can be fun to use, but I know that they don't always fit people's criteria.
If you get in the unfortunate situation of facing a Peach as Icies, channel the soul of Wobbles, but you know this already (although you seriously should take some ideas of how he plays the bad MU).
Just wanted to cover as much as possible, so you'll have to excuse the long post (at least for answering a question).