I used the prefilled syringes - and a blue ice bag on a few long term trips out.
As long as they stay COOL - not frozen - they will be alright.
Just FYI usually the company that makes PEGASYS - offers and provides you a special "lunch" type box or bag with a "blue gel or clear gel" packet - and if you freeze that - it will keep it cold for about 10 hours in that lunch bag --- I used a literal BLUE ICE brand pack --- in that thermal bag - and it was fine for 24 hours.
Just thought of something else, as you are only traveling for 24 hours, a thermo bag with a blue ice pack might be enough.
I think it would be wise to buy one of those small cooler bags. Then you'll be sure.