DD was a choker. I went into cardiac arrest numerous times.
-Offer very small amounts of food at a time (not a full plate where baby can just shovel food in at will). So I would just do one thing at a time: bits of fried mushroom (because this was her favourite! At 8, she HATES mushrooms
), chopped up tiny bits of soft cooked broccoli. Cook veggies until soft. Don't risk! Grapes, cut 'em into quarters, even smaller, to be honest!
-Chop everything into the tiniest of bits. See above. 
-Say 'small bites' over and over again, on a loop. I still say it to my teen (as a joke)! Seriously. It gets through! It really does.
-Don't worry. There are no rules to eating. Eating safely is paramount between ages 1-5. I was never comfortable with giving my kids huge chunks of melon or banana or carrots. I soft cooked all veggies and everything was cut into minuscule bites, especially with DD who seemed to choke on a daily basis.
-Do talk to your GP. Just to make sure everything is tickety boo. It almost certainly is. But because DD was such a serial choker, I did seek advice from the GP.
-They will grow up and eat totally normally! Don't worry! Safe feeding does not mean you are limiting their palate or abilities to 'eat properly'. My teen does not eat super soft carrots chopped up in tiny bites. He evolved!
Your little one will too.