The written Torah does not address the issue of circumcision on the Sabbath. Gen. 17 and Levit. 12:3 merely mention the 8th day requirement as far as the plain text is concerned.
In the Talmud, tractate Shabbos, 131b (at the bottom of the page) and onward, there is an argument about Scripture's indication. Some say that the circumcision overrides the Sabbath because we have an Oral Tradition from Moses at Sinai from G-d Himself that it in fact overrides. Another opinion holds that the word "and on the 8th day" has extra emphasis due to the added letters making the phrase "and on the". (Levit 12:3). This emphasis hints to us that it must be the 8th, even if it is the Sabbath.
Therefore, if a doubt arises as to the baby's true birthday (if the baby was born Friday evening; and we do not know if it was the Sabbath or just before the Sabbath) then the circumcision is postponed to the following Sunday, because a doubtful 8th day does not override a certain Sabbath.
The Talmud also learns out that since the verse (Levit 12:2) says that a mother "conceives and gives birth" it follows that verse 3 (8th day) only applies to a birth that was delivered through the same canal it was conceived. So, a c-section baby would not have its circumcision override the Sabbath.
Orthodox Jews do not accept the Sadducee or Karaite form of Judaism to have any validity.
The Sadducees are now extinct. They lost their power base when the 2nd Temple was destroyed. If you do find anyone claiming to be a Sadducee, they are either a revivalist or a modern day Karaite at best. Therefore, little is historically known about how they would handle a specific legal question.
Karaites however, do have small and scattered modern day communities with traditions and history dating back, in some cases, for centuries. Rabbi David Nieto authored a book called "The Rod of Judgment" (written in the early 1700's in London, England) which describes a work written by a Karaite scholar named Eliyahu ben Moshe. This Karaite scholar sets down a three way argument among Karaites about circumcision on the Sabbath. 1) It absolutely overrides the Sabbath 2) It does not override the Sabbath 3) You should do it on the Sabbath late in the afternoon after twilight because it is still the 8th day, but no longer a time of Sabbath breaking culpability.
In History of the Karaite Jews by William Harris Rule, (London 1870) it is brought down that Karaites agree that a baby should be circumcised on the Sabbath because the Law of Circumcision is mentioned earlier in history (Abraham) than the Law of the Sabbath.
Yefet ben Eli, a Karaite scholar from the mid- tenth century CE, credits (quotes) Anan ben David (the founder of Karaism) as inventing the answer to the Sabbath - circumcision question by performing it late Saturday afternoon after twilight because that time is still legally the Sabbath (8th day), but without the Sabbath restrictions in force.
Rav Saadiah Gaon (Orthodox) who lived at that time ( about 882CE - 942CE) addresses and rejects that idea.
It is common for different Karaite communities to argue about such situations and respect each others right to argue and interpret. A common phrase used by Karaites is "...so is the opinion of the majority of (our Karaite) sages..."
In general, Karaites also view a baby born late in the evening after sunset, to be of doubtful birthdate. They elect to count his birthday as if it were the next morning since that will certainly cause the circumcision to be performed on the 8th - 9th day (and not the 7th - 8th).
I hope this helps you.