I'm going to break some illussions, and i'm really sorry - but I think you're wasting your time. I will explain why I think this:
Firstly, the simple fact of karting is that a cheap kart will cost you more money. Not just in the fact that as a 2nd hand kart they will have a higher running cost than a new kart in spare parts - but because you will need to invest money into it to make it competitive...
Being competetive doesnt matter?
Wrong.
You go out on a test day in what is clearly a rental kart, pottering around as quickly as a rental kart will go - you will be getting lapped every 2-3 laps by the quick guys. They will soon get really really really really really annoyed with you.
Your stated objected is to run around the track with decals on, is it to advertise to the other racers? If so, I suggest you dont annoy them by buying an old worn out rental kart.
Is it to take photos for promotional purposes? In that case OK sure, take it out once then throw it away... It'll be a lot cheaper to stick some stickers onto the kart of somebody who actually races, but it'll achieve your objective.
The purpose of this kart is for advertising, this in an industry heavily saturated with advertising to people who see you not as a billboard, but as an annoying mobile chicane.
Billboard advertising doesn't work anyway. Most racing teams don't sell space on their race vehicles, they sell value added services and throw the name on the car as a consequence - unless you have television spectators of a race series there is no benefit to the name being on the car unless it's sat on a stand at a trade show or some such.
So commercially your project is likely to do more harm to you than good. If you are serious about advertising to racing drivers then consider permission marketting methods (read up on Seth Godin books), as currently the marketplace is devoid of this.
However, if you want to race... If that's the real reason...
Then do it properly. Get a competetive kart and race, learn the art of racecraft, and enjoy a wonderful and exhillerating sport.
There is no such thing as cheap karting. If you can't afford to do it properly then it will return the most megre rewards.
A cheap kart will cost you more money per minute spent in the kart then a good competetive kart which cost you more to begin with. The only way to achieve economical karting is to have sufficient funds to do it properly. It really is a cut throat industry that discards the poor and the broken wallets without so much as a second thought.
Nothing with rental bumpers is ever going to do anything but annoy other racers on a test day... They're looking to shave off .1 of a second off their lap times and every 3 laps they're passing you... don't do it. Seriously, just don't. It'll be the most expensive failed experiment you ever did.
Rental karts aren't just slow because of a restrictor on the engine, they have thicker and heavier chassis, more bumpers, and years of bodged repair jobs... I've seen rental karts straightened by wedging them into metal stairs and having 3 guys bounce up and down on it...