These razors come stock with an on/off controller, basically just a relay and a current limiter.
To have a current limiter, they must have a "real" controller (that does PWM, etc), which would be able to be variable (that's how the current limiting works, too), so there would be no reason to not have it be variable by throttle.
Unless it just turns off whenever current is above it's limit, which isn't useful because it would shutdown on just about any startup from a stop, etc. which is a primary place for the limiting to be required.
If it's just relays, it can't do limiting unless it also has some electronics to turn the relays off whenever the current is exceeded, but as noted that will happen on startups, etc., and make it a bit pointless to use.
Also wouldnt using a golf cart controller give too much current to the motor, and possibly overheat it? Or can I modify it so it gives the proper power for a 500w motor?
Depends on the controller, and your load and usage / conditions.
The motor will only use as much power as the conditions and load demand. If you are putting enough load on the motor that it could use much more power than it is designed for, for long enough to be a problem, you probably need a bigger motor (and battery) anyway.
You can experiment with various calculators and simulators such as the ebikes.ca motor and trip simulator, etc., to see about how much power it should take for your riding conditions and load (it doesn't really matter what system you setup in the simulator, the approximate power requirements are about the same.
The gearing of the motor to the wheel vs the speed you want to use it at also makes a difference. If it's geared too low it won't reach the speed you want without increasing the system voltage proportionally, and if it's geared too high it will waste more power and heat up more when used at lower speeds at high loads.