I might not be the most qualified person to do this, but there should be a cannonless route on this site. Feel free to post a better version or suggest fixes/improvements. (Edited a bit by @R0main )

1-1 1-2 1-3 Star House 1-Tower 1-4 Goombaless Manipulation: https://pastebin.com/Erp4vD6s 1-6 1-Castle 2-1

[Optional: if you want backup propellers during your run, The red house can give you 2 propellers (any W2 house pattern can give you 2 prop at most. ( Red house patterns list ). If you're comfortable without backups you can go directly on 2-3 but that's means you need to play 5-3 to get your propeller back after World 4. Only W2 can give you that amount of propellers, whatever the rng is but you're feel free to route extra houses. This tip is recommended for runners who begins on this category.]

2-3 2-Tower 2-4 Secret 2-Castle 3-1 3-2 Use Star 3-Tower 3-4 Secret 3-5 Red Switch 3-4 3-Castle 4-1 Hope for Fishless 4-2 4-Tower 4-4 4-Boo House Secret Star House 4-Castle 4-Airship 5-1 5-2 or 5-3 5-Tower 5-4 5-Boo House 5-5 Death (to change the vines, if you died in an other place before 5-5, death abuse can be skipped) Use star 5-Castle 6-1 6-3 6-Tower 6-5 Secret 6-Castle 6-Airship 7-1 7-2 7-3 7-Tower Secret 7-6 7-Castle Secret entrance 8-1 8-2 Secret 8-7 8-Airship 8-Castle