Going back to first principles.
When the L&SWR opened the line (presumably 1888) only three dollies would have been provided and these would all have been red Stevens flap dollies (green when flap down = "off"):
4 requires points 9 reversed (but 9 could only be reversed with points 10 reversed)
5 requires points 6 reversed
13 (your later 13-PULL) requires points 7 reversed
Despite being red, they would have been passed during shunting moves providing the relevant points were normal. [A few companies would have cleared the dollies for such movements but such locking tables as I have seen suggest that the L&SWR never did.] At some time in the Edwardian period*, the L&SWR started to use dollies with red arms for new works but there are virtually no clear photos of these and there doesn't seem to have been any programme to replace in-situ Stevens flaps.
This would almost certainly have remained the situation at the beginning of the Southern Railway period (and, anyway, yellow dollies did not yet exist), but parallel to the grouping process various committees had been considering proposals for "standardising" signals. Eventually UQ semaphores were one result of this process, yellow dollies were another, and, on the Southern both started to appear in the mid- to late-1920s, changes whose implementation is very difficult to date precisely from photographs. At the same time or probably a little earlier, the Southern started to use the familiar standard Westinghouse dolly, at this date with a red (with white vertical stripe) arm rather than with the later white and red cropped disc (which was in fact bolted on to the arm). Photographs suggest that there was an ongoing programme to replace the old Stevens flap discs ahead of the actual need to replace them because of wear/failures, (but in fact this programme was never quite completed, a few flaps remained until line/yard closure in the BR period). Some time in the 1930s (the earliest photo I can quickly find is 1936) the familiar cropped white/red disc appeared and these very quickly replaced the red arm (although again small numbers were missed and the odd red arm could still be found in the mid-1960s). Where dollies could be passed when "on" yellow arms began to be used instead of red ones from some time in the late-1920s, perhaps as early as 1926, but the photos you have found of Sway show that even this programme missed some locations (suggesting that some locomen's LDCs were stronger than others). Eventually, I have seen 1961 mentionned as a date but personally believe it was a few years earlier, the yellow arms started to be replaced with yellow on black discs, a programme that was certainly never completed.
On this website http://www.trainweb.org/railwest/railco/sdjr/signals.html
, if you scroll down to "Ground Signals", Chris Osment has provided sketches which illustrate these basic types of signals without actually showing every variation.
Returning to your layout, I don't believe that the signal (13-PUSH) for backing into the goods yard would have been provided before the Southern Railway period, so it was probably initially a red arm, later a red on white cropped disc, Westinghouse dolly and never a Stevens flap dolly. The opposing signal (13-PULL) and also the other exit signal from the yard (4) should both have been changed to Westinghouse dollies with yellow arms (although if the substitution was early enough, they would probably have had red arms initially - they should never have had red on white cropped discs despite your photo of Sway).
The other dolly (5) would have had the initial red arm, later red on white cropped disc, Westinghouse dolly.
Stevens flap dollies were installed during the alterations at Grateley in 1901 (in anticipation of the Bulford Camp railway) but wooden posted red arm dollies were installed on the Moon Valley line which opened in 1903. The painting style of the posts on the latter was "interesting".