No. As a matter of will, Sauron could not have destroyed the Ring.
Also so great was the Ring's power of lust, that anyone who used it became mastered by it; it was beyond the strength of any will (even his [Sauron's] own) to injure it, cast it away, or neglect it. So he thought. It was in any case on his finger.
But let's assume that Sauron somehow did muster the will to destroy the Ring. Let's speculate and imagine what might have happened.
The idea of beings putting their strength and power into external objects whose like can never be made again is common in Tolkien. Not just the One Ring - all Middle-Earth was Morgoth's Ring, Feanor put forth his power into the Silmarils, Yavanna put some herself into the Two Trees, etc.
The Ring and the Two Trees were, of course, destroyed. But consider the Silmarils:
Then he began a long and secret labour, and he summoned all his lore, and his power, and his subtle skill; and at the end of all he made the Silmarils.
(Of the Silmarils and the Unrest of the Noldor)
But Fëanor spoke then, and cried bitterly: For the less even as for the greater there is some deed that he may accomplish but once only; and in that deed his heart shall rest. It may be that I can unlock my jewels, but never again shall I make their like; and if I must break them, I shall break my heart, and I shall be slain; first of all the Eldar in Aman.’
(Darkening of Valinor)
It isn't quite as clear-cut as the case of Sauron and the Ring. We aren't explicitly told that Feanor would have died because of the power he put into the Silmarils; you could believe that he would simply be that sad about it. But if it is because of the power he put into the Silmarils, then Feanor doesn't seem to believe it's possible for him to simply "reabsorb" that power, because if so, you'd think he could simply remake them afterwards.
So I would guess that even if Sauron could bring himself to destroy the Ring, no matter how he went about it, it would kill him. Power, once externalized, is forever out of your control.
I should say it [the Ring] was a mythical way of representing the truth that potency (or perhaps rather potentiality) if it is to be exercised, and produce results, has to be externalized and so as it were passes, to a greater or less degree, out of one's direct control. A man who wishes to exert ‘power’ must have subjects, who are not himself. But he then depends on them.
This would also echo Morgoth, who spent all his will and power in mastering Middle-Earth to the point that the whole world became Morgoth's Ring - but Morgoth himself was diminished and got whooped by the Host of the Valar, despite once being the mightiest of the Ainur. You'd think if he could have ceded some of Middle Earth to regain the power to defend himself, he would have done so.
So I'd say Sauron could regret all he wanted - he sealed his fate the day he made the Ring. Which ended up not even working like he wanted. Sucks for him!