If one Davened an extra-long Shemoneh Esrei, and missed saying ויכולו... with the congregation, can he say it by himself? Or must he say it with someone else?
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The Avudraham says that we repeat Vayechulu because we are testifying that G-d created the world in 6 days and rested on the 7th. The Halacha is that testimony must have two witnesses and be said standing, and therefore Vayechulu is said together while standing.
The Shulchan Aruch Harav, in his Kuntres Acharon to Orach Chaim 268:12, brings the opinion of the Taz that someone praying alone doesn't have to say Vayechulu standing, since it's not real testimony. Although the Rav concludes that the custom is to stand even if it is not real testimony, we see from there that he held that someone praying alone could say it.
The Shaar HaKollel brings the Tola'at Yaakov who questions the Avudraham's claim that we are giving testimony. One of the arguments brought is that it is against Halacha to give or accept testimony at night, so this isn't real testimony.
The Shaar HaKollel and Tola'at Yaakov also bring other reasons why it is important to say Vayechulu twice in the evening service (3 times with Kiddush), as does the Avudraham.
All that tells us is that one may say it alone. If however, you have easy access to someone else who can say it with you, it may still be better to say it with someone else.
The position of the Chazon Ish is that Vaychulu is part of davening, not testimony, and therefore it's preferably said alone, if one is not part of a minyan. Ask your local rabbi, or follow local norms.
He can say it by himself, but he should try to say it with another person. The reason that the mitsva here is of testimony, so reading out loud with someone else one would fulfil the mitsva of testimony, while reading alone it would simply count as you were reading any other pesukim.