Step 1: Recall excretion in the cockroach.
The main excretory organs of the cockroach are the Malpighian tubules. Other structures like fat bodies, uricose glands, and the cuticle also help.
Step 2: Check statement I.
Each Malpighian tubule has two parts. The distal portion, away from the gut, carries out secretion of waste. So statement I is correct.
Step 3: Check statement II.
Fat bodies store extra uric acid inside the body instead of throwing it out at once. This is called storage excretion. So statement II is correct.
Step 4: Check statement III.
In male cockroaches, the uricose glands store uric acid and release it onto the sperm during copulation. So statement III is correct.
Step 5: Check statement IV.
Statement IV says the cuticle has no role in excretion. But some waste is dumped into the old cuticle and thrown off during moulting. So statement IV is wrong.
Step 6: Combine the correct statements.
Statements I, II, and III are correct, while IV is wrong. This matches the third option.
\[ \boxed{\text{I, II and III}} \]