Actually members of securityadmin can do anything I believe, as it is in their powers to elevate themselves to sysadmin...
That aside, let's try it:
CREATE CREDENTIAL credo WITH IDENTITY = 'ident', SECRET = 'Hemligt!'
go
CREATE LOGIN secadmin WITH PASSWORD = 'dfghhh'
go
ALTER SERVER ROLE securityadmin ADD MEMBER secadmin
go
EXECUTE AS LOGIN = 'secadmin'
go
ALTER CREDENTIAL credo WITH IDENTITY = 'newident', SECRET = 'Hemligare!'
go
REVERT
go
DROP LOGIN secadmin
DROP CREDENTIAL credo
Nope:
Msg 15151, Level 16, State 1, Line 1
Cannot alter the credential 'credo', because it does not exist or you do not have permission.