I think to make him a jungler, we'd have to hone his kit a little. I think his core tools, the ones that make up his identity, are stealth, blinding, and vision control. DOT with poison and swiftness are also relevant, but moreso due to his lore/title than interesting gameplay.
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If we shape his kit around those concepts, we might get something that looks like this:
Passive - Teemo gains an MS burst after using an ability.
Passive - Teemo's autoattacks apply poison.
Q - Toggle blowdart/knife. Upon first auto after toggling: blowdart blinds and deals extra damage, knife slows and deals extra damage. Dart has more range, knife has more damage and higher base AS. Fairly low CD.
W - in essence, a scrying orb. Works linearly, as it would be based on his telescope.
E - now toggles stealth. Applies immediately. Lasts until Teemo moves. (CD tbd; while I like the idea of teemo sneaking from bush to bush and quickly restealthing in each, that might be too strong). His passive applies to this ability AFTER he exits stealth.
R- About the same. I'd lower the damage and also lower the CD, so it's more about vision and less about burning half of someone's health without any realistic play/counterplay.
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I worry about the damage in this kit not being high enough, but I think his Q and his poison damage on autos can be adjusted.
I also worry, more relevantly, that this is not a jungle-centric kit necessarily. I think it fits him better, provides more interesting play/counterplay, and really gives him a solid core identity; but I don't know that it wouldn't be abusable elsewhere (top lane, support?).