I've been riding around for the last month and a half brakeless and I barely put on a front brake last night.
Problem is today as I was doing my commute I noticed my steering felt strange. I didnt think much of it until I went to reach for something and was riding with no hands, the bike's steering began to wobble. Is this from the unbalance in weight from having only one brake lever on?
It didnt really affect me, but it makes me a little nervous just knowing something might be up.

Cable too short? Cable too long?

why would this matter?

The weight imbalance will have a negligible effect on your steering, or really anything for that matter. Chances are either you have some brake rub or your wheel is not centered or is out of true.

I have no idea, I havent run into any issues with my cable length I can go into my LBS and ask if it is the length.
How would cable length affect the bike's handling?
At the very least I installed the brakes correctly and now just in case I can stop pretty quickly now.

My front wheel is going out of true, I'm hoping my wheels hang in there for the next week or two because I'm going to order new wheels. I'm trying to keep it as true as I can get it til then.

Maybe your stem isnt tight enough on your headset. That would cause the handlebars to be off from the fork.

What kind of bike is it and how old? My old conversion felt the same way until I had the steerer tube faced and put a new headset in.

Installing a brake has obviously made you lose your mojo.

Were you on a bumpy road? Was it windy? If your wheel is out of true it could definitely cause the wobble. True it and see if the problem goes away. It might have something to do with the geometry of the bike too. Some bikes I can go around corners no-hands, others I can't even take my hands off the bars or I'll veer off course immediately.

Nope.

Sounds most like a headset issue to me.

Don't just check the tension/true of the front wheel.

An out of true / poorly tensioned rear wheel can cause the wobble you are experiencing as well.

+1

Make sure you preload the bearings and then snug your stem. I don't mean that to be condescending, btw.

instability is an attribute, unstable is a condition.

and yes, headset is a big culprit and the first thing to check.

It did occur to me that I used the wrong word, I tried to change the title and failed.

I ordered some new wheels so I'm going to see what happens when they come in.

It has in come cases, but I have noticed that I've been better at track stands since then.
The brakes make for a good laugh when I try to see how fast I can ride indoors at work.