Wales were hammered by New Zealand on Saturday.
The Six Nations champions have little time to dust themselves down before World Cup holders África do Sul arrive in Cardiff next Saturday.
UMA 54-16 defeat against New Zealand – the All Blacks scored 26 unanswered points during a ruthless final quarter – was Wales’ 32nd successive loss in the fixture since 1953.
It was also the most points they have conceded to any opponent for 14 anos, with England racking up 62 against them during a 2007 World Cup warm-up mismatch.
Northampton fly-half Biggar and Gloucester wing Rees-Zammit were among seven players unavailable to face New Zealand because the game took place outside World Rugby’s autumn international window.
Along with the likes of Saracens centre Nick Tompkins and Wasps flanker Thomas Young, they will now join the squad for Springboks preparations, while Wales head coach Wayne Pivac awaits fitness updates on several other players.
The casualty count ran into double figures ahead of facing New Zealand, and that list increased when captain Alun Wyn Jones and flanker Ross Moriarty both went off before half-time due to shoulder issues.
Initial assessments point to Moriarty’s injury being considerably more serious than the skipper’s, with Jones set to win his 150th Wales cap if he is declared fit for South Africa, while Liam Williams, Ken Owens, Ellis Jenkins and Taulupe Faletau are among those on Pivac’s check-up radar.
“It was a good experience for some guys who hadn’t played at this level for a while,” Pivac said, reflecting on the All Blacks game.
"Agora, we’ve got players coming back in, and we will settle on a squad early next week for South Africa.
“We will get them in and assess them on Monday and see who is fit to go.”
Recalling the All Blacks’ devastating late try blitz, Pivac added: “Clearly, the last 20 minutes showed the difference between fitness levels.
“You are talking about a side that has been playing international rugby on the road for a couple of months.
“That was the conversation Ian Foster (New Zealand head coach) and I had afterwards. We fell off a cliff.
“Some boys have only had a handful of club games. We’ve got some work to do in that area. It won’t come overnight, but we will work hard before the next opponent.”
Wales’ undoubted highlight was the performance of 21-year-old Dragons flanker Taine Basham, who excelled on his first Test match start and gained a glowing review from Pivac.
“Taine Basham was our man-of-the-match,” Pivac said. “He is a young guy whose confidence will go through the roof, and he is now an extra player we have at this level.”
For his part, Basham looked like a Test match natural just four games into his international career.
“I just play my game. Nothing changes for me, I don’t think,” said the Dragons academy product, who emerged through grassroots Welsh clubs Talywain, Bedwas and Cross Keys.
“I go into the game with the same attitude. Even if I wasn’t playing an international, I just go into every game giving it my all.
"Obviamente, the seven jersey in Wales is always competitive. For me, I just play my game, and I play with quality players.
“We just need to bring it next week and go up another level. I think we have got another gear in us to go up again, so I am looking forward to it.”