England have been plagued by injuries and flu in South Africa and the situation has worsened with opening batsman Rory Burns picking up an injury during practice.
South Africa registered a 107-run victory in the first Test against England, which also ended their run of five successive Test defeats.
Jos Buttler also said he is looking at South Africa wicket-keeper batsman Quinton de Kock for inspiration.
Archer bowled only six balls during training on Wednesday in Cape Town before the elbow acted up, raising concerns as to whether he can recover in time for the second Test which will start on Friday.
On Tuesday, England coach Chris Silverwood hinted that either Anderson or Broad might be dropped for the second rubber to make room for a spinner.
James Anderson recently recovered from an injury and played his 150th Test match in Centurion against South Africa, which England lost by 107 runs.
The tourists still need 255 more runs to win but have one of the most improbable come-from-behind wins in test history - from the Ashes series earlier this year - fresh in their memory.
Buttler couldn't take the gloves at the start of Day 3 of the first test on Saturday and Jonny Bairstow stood in. Bairstow is also a specialist keeper and has kept wicket in tests before.
Cricket South Africa said that the injury took place during Day 2 of the ongoing Test against England and will require surgery which will keep him away from the game for at least six weeks.
Stuart Broad, Anderson's long-time pace partner, and newcomer Sam Curran followed up as South Africa struggled to 111-5 soon after lunch before recovering.
James Anderson, 37, made a terrific comeback as he scalped Dean Elgar with the very first ball he bowled.
Fast bowlers Stuart Broad, Jofra Archer, Chris Woakes and spinner Jack Leach have all contracted a flu-like illness which is spreading in the team.
James Anderson is likely to return to the side for the first Test of the four-match series against South Africa, starting on Boxing Day at Centurion.
In an official media release, the England and Wales Cricket Board (ECB) said that due to widespread illness in the England camp, it has been agreed that the match against South Africa 'A' starting at Willowmoore Park on Friday
While Malan and Second are uncapped at the international level, Dane Paterson, Rassie van der Dussen, Beuran Hendricks and Dwaine Pretorius, who are all yet to make their Test debuts, have played white-ball cricket for South Africa.
Ngidi has been diagnosed with a "significant Grade 1 hamstring muscle tear", which he picked up during warm-ups ahead of the Mzansi Super League play-offs, Cricket South Africa confirmed on Sunday.
South Africa were thrashed by 104 runs by favourites England in the opening match of the ICC World Cup, which began at The Oval on Thursday.
Dishing out a clinical performance in all three departments, South Africa had no answers as Ben Stokes and Jofra Archer starred in England's 104-run win in the tournament opener.
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