Corn syrup is often used in candy making to control sugar’s tendency to be grainy and to crystallize. We think several other liquid sweeteners would substitute nicely. Golden syrup, a pale derivative of the process of refining sugar cane, is our best suggestion. Other options include the rice syrup you mention or barley malt syrup.
We’d stay away from honey, though. First, it has a lot more flavor than corn syrup or the other choices and might overpower whatever fruit or mint flavors you’d choose. Second, it tends to soften candy, because it attracts moisture.
The final option is a simple sugar syrup (essentially omitting the corn syrup in your recipe), which you can easily make yourself. If you have a trustworthy candy thermometer, you can take it to the ideal temperature (300°F to 310°F (150°C to 155°C)) for lollipops and other hard candies.