Assad Fudadin and Marlon Samuels will both be available to face England Lions on Thursday after finally arriving in the country.
Fudadin was the latest of a 15-man squad to set foot in England this summer, his journey from the Caribbean completed on Wednesday - 24 hours after Samuels' arrival from the Indian Premier League.
The duo's arrival means the West Indies are now only one short of a full complement of fit players with Fudadin's fellow Guyanese Narsingh Deonarine the last of the squad to join up for the forthcoming three Tests against England.
All-rounder Deonarine was expected to accompany Fudadin, having experienced the same visa hold-ups as his compatriot and still waiting in Jamaica for clearance to fly.
But whereas Fudadin's documentation allowed him to travel on Tuesday night, it is now hoped Deonarine - far the likelier of the two to be in the Windies' Test match plans - will arrive on Thursday.
Even that would rule him out of the reckoning to face the Lions in Northampton - the Windies' second and final warm-up match before they head for Lord's next week - unless forecast rain arrives in bucketloads to delay proceedings.
Asked the reason for Deonarine's ongoing delay, a team spokesman said: "It's the same issues, processing.
"Once the process is finished, he'll be on the flight."
West Indies, beset by bad weather in preparation for and during their opening tour match at Hove, were again restricted to indoor practice on Wednesday afternoon as rain - absent while the Lions netted in the morning - fell at Wantage Road.
But the tourists were able to report both batsman Shivnarine Chanderpaul, who needed treatment to a bruised hand against Sussex two days ago, and paceman Fidel Edwards - having rested a back "niggle" on the south coast - are both fit.
The spokesman added: "The issues with Shivnarine Chanderpaul were a little exaggerated, and we'll continue to monitor Fidel (Edwards).
"So everyone [here] is available for selection."