Bokker makes some knives like that, but I've always been partial to flippers like the CRKT M21. Does it need to have an actual button? That might limit your choices a bit.

If legal for you to purchase and own (important, these are different distinctions), an automatic knife would be the safest for one handed operation. Anything from the Kershaw Launch line will be bulletproof and have decent steel.

Non-auto non-assisted button locks (the type of knife you asked for) are kind of niche. Kizer makes some decent ones, and Civivi makes the exact razor blade utility knife you’re looking for, but in higher quality and within your budget.

Otherwise I gotta say, if you’re not a current knife enthusiast, look for sales on Benchmade Griptilians (or mini-griptilians). The Axis lock is not exactly a button press but if you want higher quality, it’s a good option.

A button lock knife is very popular. Many are well under $100. I'd recommend the CJRB Pyrite Alt for a blade shape more similar to a razor. if you want even smaller the Mini Pyrite Alt is a great 5th pocket carry. https://www.knifecenter.com/kc_new/store_store.html?steel=AR-RPM9&style=Wharncliffe&usrsearch=pyrite&sortType=priceAs

you can do the same using any knife with a "button lock".

most popular knife of the last couple of years has a button lock variation and it's less than a $100 https://www.knivesandtools.com/en/pt/-civivi-elementum-button-lock-c2103d-stonewashed-brown-micarta-pocket-knife.htm

Always been a fan of butterfly knives.

https://www.bladehq.com/cat--114-Butterfly--2423

If you don't know how to use one, make sure you put masking tape on the edge until you're comfortable with it.

You can buy dull trainers too.

You might also look at knives with an Axis-lock type system. It's not identical, but rather than a button press you slide a stud with your finger, so it has the same easy one-handed opening and closing. That used to be limited to Benchmade, but it's now available pretty much everywhere. I really love my Kershaw Iridium: https://kershaw.kaiusa.com/iridium.html

https://www.milwaukeetool.com/Products/Hand-Tools/Cutting/Knives-and-Blades/48-22-1990 Milwaukee makes one, in several sizes and blade shapes even.

I bought one to cut down on waste with disposable blades and it works great for tearing up packaging and boxes. The steel is supposedly pretty soft, but it's also around 20 bucks depending on size and blade shape.

The non assisted opening mechanism is probably my least favorite thing about the knife, if I'm honest, but it's not horrible or anything.