The exposed chalky bits of the Ridgeway can be treacherous after light rain as it does become very slippery. There’s not much that can be done about it being that it is just the local geology being exposed. Top dressing it won’t help as it would soon be eroded to expose the chalk again.
I know the section well and unfortunately it just needs extra care after rainfall. Tyre choice and running a lower pressure should help in those situations. There is actually a worse bit if you follow the course of the Ridgeway from where you describe towards Streatley (the “chalk and flint climb”). Its a great commute route though in dry conditions.