You used to sit next to them. You have not, for years. You want an intro to someone they know. The draft that feels earned writes as if you still share a slack and a badge. You do not. The product will not pretend you do either.
A warm history is a fact about the past. An accepted contact is a fact about the channel. Keep them straight.
Be honest about the door you are using
If they have never activated a RelayLink account, the send is email and a page. That is allowed. It is still a first contact, with a daily cap, and the refusal if they already have an account will not tell you which you hit. You are not owed a side channel because you used to be on the same team.
If they do have an account, invite them and wait. You cannot accept your own request. The invitation carries no note — on purpose. Do not try to smuggle the intro into the request. Ask after they say yes, or send the intro as ordinary email if this is a one-off.
Do not write as if you are already on a thread you do not have.
Give them a note they can forward
Write for a cold reader: the person they would introduce you to. One paragraph they can pass along without editing. Who you are now, what you want, why this person, what you are not asking for.
Then the ask of your former colleague, separate: will they forward that paragraph, or not. An easy no. "If this is a bad time or a bad fit, a one-line no is enough and I will not follow up."
Do not make them write the blurb. People skip intros they have to author. Do not make them sell you. People skip those too.
You still approve the words
An assistant can draft the forwardable paragraph. You read it. A private nickname from the years you worked together does not belong in a note they will send to someone else. Use the name they use now.
They need nothing installed to read this. You do not need their current company's Slack. If they reply from the page, that is the channel until they choose an account.
If you already told an assistant the story of the old team, connect it and have it write the forwardable paragraph as if the third person has never heard your name. They have not.