I’m curious what you mean by this. Most of the guys I know treat their Instagram accounts like their LinkedIn accounts: It has enough information and occasional updates with major life changes, but they don’t actively engage with it all the time. Just let it exist and respond to any messages if they come in. Would that work, or are you saying the dating scene in your area requires some type of active constant engagement with Instagram?
Some level of engagement with it, anyway. Only having one post from 7 years isn't going to do you want favors, but I'm not saying you need to be on it 97 hours a day either. But the younger crowd seems to favor that app as a first level of contact, and you can escalate (as welcome) from there.
If you steadfastly refuse to have one, it seems like it'd be the same as trying with job seeking without a LinkedIn. Which you can do, but it seems like making things harder than they need to be when things are already difficult.