Need adventure map help

The problem is that the player is the one who is running the command with JSON commands. One possible workaround is the /trigger command:

Before anything else, once:

/scoreboard objectives add TalkToWoundedGuy trigger
/summon ArmorStand ~ ~ ~ {CustomName:"O"}

On a repeatingCommandBlock/chainCommandBlock loop, in order:

/scoreboard players enable @a TalkToWoundedGuy
/execute @p[score_TalkToWoundedGuy_min=1] ~ ~ ~ execute @e[name=O] ~ ~ ~ [all the 'say' commands you want, on different command blocks]
/execute @p[score_TalkToWoundedGuy_min=1] ~ ~ ~ [all the other commands you want, on different command blocks]
/scoreboard players set @a TalkToWoundedGuy 0

On the sign:

{Text1:"{\"clickEvent\":{\"action\":\"run_command\",\"value\":\"/trigger TalkToWoundedGuy set 1\"}}"

You should use the /tellraw command instead of /say for greater control of content.

For example, you would cause the player to run the following command:

/tellraw @a {"text":"[Wounded Man]: A storm's coming I suggest you find shelter..."}

Output:

[Wounded Man]: A storm's coming I suggest you find shelter...

You /give command would instead become:

/give @p sign 1 0 {BlockEntityTag: {Text1: "{\"text\":\"Wounded Man\",\"color\":\"red\",\"clickEvent\":{\"action\":\"run_command\",\"value\":\"tellraw @a {\\\"text\\\":\\\"[Wounded Man]: A storm's coming I suggest you find shelter...\\\"}\"}}",Text2: "{\"text\":\"Click to talk\",\"clickEvent\":{\"action\":\"run_command\",\"value\":\"say New Quest: Find Shelter\"}}",Text3: "{\"clickEvent\":{\"action\":\"run_command\",\"value\":\"particle fireworksSpark\"}}"},display: {Name: "Custom Sign"}}