Cockpit-drain hoses
I use only Shields '148' PVC hose for underwater connections including cockpit drains. It's the same hose as marine toilets are hooked up with only in different sizes. You know it by the slight ribbing and white color. It is not cheap-- but I would NOT use clear plastic aquarium hose or engine heater hose for this application and NEVER that flimsy white plastic 'vacuum-cleaner' stuff-- not for seawater (never, never NEVER).
Shields 148 is a bugger to work with-- it will fight you both going on and off. I use dishwashing liquid and a heat gun. This does wonders. You can use a hair dryer instead; but squirt a little dishwashing liquid into the end of the hose first. As soon as the hose gets warm in your hand shove it onto the hose barb. Don't forget the hose clamps (did, learned that lesson).
Make sure you make your hose runs as short, as straight, and as uncomplicated as possible. I don't like the T-fitting idea but if you have only one through-hull it'll have to do. Consider using a Y-fitting, not a T which can easily become clogged with pine needles and other junk (and will be harder to unblock). Don't buy a cheap nylon one but seek the better black PVC ones or Marelon. (The through-hull should not be nylon either.) Double-clamp all hose connections within 6" of the at-rest waterline, even far from the through-hull.
Do you have a shut-off on this through-hull? Prudence dictates that if it's within 6" of the at-rest waterline it should have one. Forespar makes a very good inline shut-off ball valve in Marelon that's not too expensive. Remember through-hulls (and all Forespar Marelon fittings) are straight threads, not standard plumbing threads, so stuff from HoDePo won't work here (tried it, learned that lesson). I don't like 'brass' ball valves; most of them have a steel ball, steel handle and/or steel shaft and will magically become rust in very short time.
Also remember that no other drains should dump INTO the cockpit if your cockpit is dependent on hoses, hose clamps, through-hulls and seacocks/ball valves for drainage. If it's a direct-overboard scupper (like with an open transom) it's another matter.