Saving Yardage

I have a pattern I would like to make with a particular skein, but I’m about 25-30 yards short (need 450, have 425 – I was too cheap to buy a whole other 400+ yard skein just for those few more yards). The ladies at the yarn shop said that I could save yardage by going up a needle size to make it less dense, without modifying the pattern. Is this right? It seems to me that I would use less yardage by going down a needle size and making smaller stitches around a thinner needle. I am petite and the pattern is for a shawlette that I am more likely to wear as a scarf so I am not concerned if it comes out a little smaller than intended. Thanks in advance for letting me know what you think!