OP, you may not think you're that risky, and maybe you aren't but you probably have a shorter track record. I too have made all of my payments on time, but I've done so on maybe 5 different mortgages, ~50 credit cards, 1 student loan, 1 bank personal loan, and every single rent payment. Over the past 26 years.
(The nice thing is, if you keep it up for another 20 years, you'll almost have bankers paying you to borrow money.)
That having been said, your idea is perfectly sound as long as you account for the following factors:
1. You'll probably pay some sort of origination fee on the new loan, which will cut into your interest savings. Probably 1% to 3%, depending on if you do a personal bank loan or a credit card.
2. The payback term will most likely be shorter than your current loan, which will mean higher payments, which may not be a problem in your case since you're doing large additional payments already, but I would look at it as a little loss of flexibility in your financial arrangements.
3. Deductibility of interest. Student loan interest is often tax-deductible; a private loan would not be.
4. Student loans often have some flexible payment features like forbearance and suspension and such. Private loans and credit cards don't. Again, probably just a flexibility-limiter here.
Overall, you'll probably find that you can save some money at the cost of flexibility. Were I in your shoes I'd probably make the trade, especially if I could get a zero fee balance transfer to a credit card. But that's for you to decide. Good luck.
(In fact, I did something similar -- had both the option to take student loans to pay for my schooling and then had scholarship help, so I used the student loans to pay for school at 0% interest while in school then something ridiculous like 2.9% fixed at graduation, and used the scholarship funds to pay down my mortgage which was at ~7% at the time. Another time I borrowed about $500K on zero percent credit cards for a year and was earning more interest than I was paying on my mortgage for about a year. So things like this can be done and are worth your while if you can pull them off.)