Translation:I don't want to say it out loud.
I know Duo's tips section says chūlái, but Yellowbridge dictionary says:
出来 (chūlái) is a verb: to come out; to appear; to arise
出来 (chulai): (after a verb, indicates coming out, completion of an action, or ability to discern or detect)
I feel like 出来 in this skill is actually being used after verbs with the second definition (chulai) meaning coming out.
Can any native or advanced speakers offer their opinion?
出來 are linked here. "Come out." 说出来 means that the speach is actually coming out of your mouth.
Look on Google for examples of directional compliments in Chinese. You should also look other verb compliments while you're at it. Like 说话,洗干净,etc. Those are similar.
Also, pro tip: any translation of these like go out, come over, go in, come in, are basically the reverse of what we say in English. 出去,过来,进去,进来。