There were several alternatives - but no obvious reason to prefer any of them to James.
i) Lady Arabella Stuart. She was James' cousin, and unlike him had been born in England, which some lawyers held to giver her a better claim to the throne. There were various rumours of plotting on her behalf, and she died in the Tower.
ii) Edward Seymour, Lord Beauchamp. He was the son of Catherine Grey, sister of the unlucky Lady Jane. Under henry VIII's will, which gave preference to the heirs of his younger sister Mary, Beauchamp had an arguable claim, but in 1403 still hadn't secured recognition of his legitimacy (his mother's marriage had been clandestine). A son of his did a similar secret marriage to Arabella Stuart, but was luckier than his bride and eventually managed to mend his fences with the King. After that they gave the stuarts no trouble.
iii) Lady Anne Stanley. Descended from Mary's younger daughter, she inherited that claim if Beauchamp was considered a bastard. Afaik though, she never made any claim to the throne.
There's no knowing whether any of them would have ruled better than the Stuarts, but in any case it would probably have meant losing the union with Scotland, which might have emant more wars with that country.