only a bris that is on time on the eighth day is done on shabbos (ch 19 mesechta shabbos), so a mohel who performs a belated bris on shabbos is mechalel shabbos, does that invalidate the bris being that it was done "illegally"?
Mishna Shabbat chapter 19 verse 4:
מִי שֶׁהָיוּ לוֹ שְׁתֵּי תִינוֹקוֹת, אֶחָד לָמוּל אַחַר הַשַּׁבָּת וְאֶחָד לָמוּל בְּשַׁבָּת, וְשָׁכַח וּמָל אֶת שֶׁל אַחַר הַשַּׁבָּת בְּשַׁבָּת, חַיָּב. אֶחָד לָמוּל בְּעֶרֶב שַׁבָּת וְאֶחָד לָמוּל בְּשַׁבָּת, וְשָׁכַח וּמָל אֶת שֶׁל עֶרֶב שַׁבָּת בְּשַׁבָּת, רַבִּי אֱלִיעֶזֶר מְחַיֵּב חַטָּאת, וְרַבִּי יְהוֹשֻׁעַ פּוֹטֵר: [The amoraim differ in the gemara as to the correct version of this Mishnah. The version subscribed to by my rabbis is the essential one, viz.:] If one had two children to circumcise: one, after Shabbath; the other, on Shabbath, and he forgot and circumcised the first on Shabbath, and the second after Shabbath, he is liable (for a sin-offering). (If he had) one to circumcise on Sabbath eve, and the other on Shabbath, and he circumcised the first on Shabbath, R. Eliezer rules that he is liable for a sin-offering, and R. Yehoshua exempts him. [This is the interpretation: If he forgot and circumcised the after-Shabbath child on Shabbath, all hold that he is liable. For he erred in the performance of a mitzvah and did not perform a mitzvah when he circumcised the after-Shabbath child on Shabbath. In this, even R. Yehoshua concurs. ("one to circumcise on Shabbath, and one to circumcise on Sabbath eve, and he forgot and circumcised the Sabbath eve child on Shabbath, R. Eliezer rules that he is liable for a sin-offering":) For milah beyond its time does not override Shabbath. And even though he erred in the performance of a mitzvah, being taken up with the Shabbath circumcision, for which reason he erred with the other — and even though he performed a mitzvah even with the first, for he was fit for circumcision, though not for circumcision overriding Shabbath — R. Eliezer holds that if one erred in the performance of a mitzvah and performed a mitzvah which does not override Shabbath, he is liable. ("and R. Yehoshua exempts him":) He holds that if one erred in the performance of a mitzvah and performed a mitzvah which does not override Shabbath, he is exempt; for he felt that he was operating under the sanction of beth-din. The halachah is in accordance with R. Yehoshua.]
I have highlighted the significant text where Rabbi Yehoshua, according to whom the halacha follows, exempts him from bringing a korban chatat because he has fulfilled a mitzvah.
Ergo, the milah is valid (unlike the other case discussed here).