I know in the past, there was quite a concern for Score Sending because it leads to freezes, is it still as much of a risk now that Jumpstart has taken over?
Pretty much what Hikimaru said. Use safe times and scores, don't scoresend too much in one day, etc etc. Usual smart safety precautions and you'll be fine.
Additionally, regarding the JS thing: Yes, it is also safer now after JS took over. With JS's leniency (or perhaps just lack of staffing), you can even scoresend for hours everyday and you won't get frozen. Right now the thing that mainly gets people frozen is reports from legit users instead.
Don't take that as a recommendation to scoresend for hours though lol. No one plays Neopets games non-stop for many many hours without breaks, and also scoresending is not particularly worthwhile anyways. You're better off ABing really, even without Advanced.