Pre-ejaculatory fluid is not what you need to worry about here. The worry would be if the pre-ejaculatory fluid carried sperm in it.
If a man has ejaculated prior to getting an erection (if he had masturbated within a few hours of getting the next erection, or if he had sex with his girlfriend and ejaculated outside her body, and then had a second erection and inserted it again, for a couple of examples), his pre-ejaculatory fluid could contain sperm. The millions of sperm produced by the prior ejaculation don't all leave the man's urethra on the first ejaculation. Some hang around in its nice, warm, moist environment, and don't necessarily all immediately die. If some new pre-ejaculatory fluid comes along in a subsequent erection, they hitch a ride in it, into the woman's body.
So, whether pre-ejaculatory fluid could last from December 26 to January 4 -- it wouldn't matter whether the pre-ejaculate could last that long or not, it would matter if there was sperm in it, and if that sperm could last that long. The research I've seen suggests that while sperm sometimes can live a week, it is not vigorous by then, and researchers doubt it would be strong enough to penetrate the egg.
Given your ultrasound's early date, I would say it probably has a margin for error of +/- 1 or 2 days. But I am puzzled about the due date. Did they give it to you, or did they just tell you the figure of 7 weeks 4 days? Because I don't get exactly the same estimated conception date from that count of weeks, I get January 3. That's not quite early enough to implicate the first guy, but only by a whisker-thin margin. If you add it to the fact that the sex with the second guy was all unprotected and he ejaculated inside you both times, it suggests the first guy is not the dad and the second guy is, but it would be close enough to make it important to get a DNA test after the baby is born, just to never have to wonder. Not that guy #1 has a strong chance, it's just not that one could say with certainty that it is a zero chance.
So you're asking if sperm can last from December 24 to January 4? No.
*the, not 'thge.'
If you do try the ultrasound route, don't delay at all. Babies grow at different rates, and while they all begin as one cell and split to two, by the time you are at your 12th week a baby's ultrasound measurement can diverge from the average by as much as a week, which would not help you because your dates are so close together. You need as much precision as you can get, and to get it, you shouldn't be using an ultrasound too much later than week 7 or 8 of pregnancy (counted from the first day of your last period).
The only thing that will possibly help you to know (besides a prenatal DNA test) would be if you would get an ultrasound right away (such as, this week), and tell the doctor that you would like to know your estimated due date from the crown-to-rump size of the embryo and its developmental markers only, rather than from the first day of your last period. (You might even say that you don't know for sure when your last period was, or that it is too irregular to count from. That way you could be certain they were using the embryo's measurements only.) They will tell you an estimated due date, and you can put that into a calculator or simply count back from it 266 days on a calendar, to reach an estimated conception date. If you are lucky, it will point to a date that can only indicate your boyfriend and not thge other guy.