I am a bit 'puzzled...
(1612 POD) In November Henry decides to take an unseasonable swim in the Thames, subsequently contracts typhoid and was only saved by the intervention of his friend Sir Walter who despite being in the Tower of London procured some Quinine to break the fever. (OTL Henry dies and Charles became the successor)
A swim in the Thames? In November???
It was during the preparations for the wedding of his sister Elizabeth with the Elector Palatine Frederick V that he fell ill: during the summer and autumn 1612 Henry was particularly occupied to arrange the visit of his future brother-in-law, because he has intention of accompanying his sister in Germany, where he wanted to choose a wife for himself.
For this reason he participated in the organization of the wedding, including the flotilla for taking the princess across the sea: probably it was at this time he contracted typhoid fever. On 10 October he was seized with a severe illness, and he had been afflicted with lassitude, and occasionally severe headaches, but he gave not sufficient importance to these symptoms: it is said that he played at tennis in chilly weather with insufficient clothing and the next day he was unable to rise from his bed, declined quickly, and died on 6 November.
Despite the best efforts of a bevy of doctors, including Theodore de Mayerne, the king's physician, Henry died.
Theodore de Mayerne was a Swiss-born, a Huguenot, and closely linked by ties of friendship and family ties to Theodore Beza.
And still: the use of quinine as malaria treatment goes back to early 1600s, precisely in 1630, when it was used by Jesuit missionaries in South America, and involved also the Spanish Countess of Chinchon, wife of the Peruvian Viceroy (in 1742, botanist Carl Linnaeus called the tree "Cinchona" in her honour).
She, or more realistically the Jesuit Bernabé Cobo (1582-1675), it on his return to Spain with the bark, may have introduced quinine to Europe around 1638.
There is, therefore, an obvious chronological problem in assuming the curative use of quinine twenty-five years before its arrival in Europe, as, indeed, that a Spanish scientific discovery was shared in advance with "heretics" English...
It was during this time that Henry was betrothed in Marriage to Maria Elisabet of Sweden daughter of Charles IX and his second wife Christina of Holstein-Gottorp
And again: among the suitors of Henry's sister Elizabeth it was also Gustavus Adolphus of Sweden, son of the King Charles IX of Sweden. Also if Gustavus Adolphus appeared a perfect match for a marriage of royal rank, he was rejected quickly because «his country was at war with Queen Anne’s native Denmark» (narrated also in Wikipedia), Denmark with which the England of James I was closely connected by strong trade links, including in the Baltic, and against the interests Swedish. It appears, then, a little difficult that the same conditions did not have value even for the wedding of the heir to the throne, and that Henry has married Maria Elisabeth of Sweden daughter of King Charles IX...
to begin...