You are hung up on deciding whether to redesign your site before you start building links to it?
It’s hard for me to answer that question without first knowing why you’re considering a site redesign in the first place.
If your current website design is stalling your brand, then I suggest holding off on building links until you get the situation rectified. The last thing you need to be doing is reaching out to people for backlinks under those circumstances.
However, if you’re redesigning the site for any reason other than brand reconstruction, delaying your link building efforts will only stall what you’re trying to accomplish on your website.
That’s how I see the matter at least.