How can Jack deliver such toys to the children?

To accompany the film, Touchstone Studio also licensed a 'Penguin Active Reader' book for younger viewers. This book was based on the Tim Burton screenplay and can, presumably be considered canon to the main film:

To answer your question, the simple fact is that Jack was blissfully unaware of the nature of the presents he was delivering.

• He didn't inspect them before they were loaded into the bag:

In Halloweentown, the vampires finished making Christmas lights— with little skeleton heads. The youngest witches finished making their toys—wonderfully dangerous toys. Jack's plans for Christmas, the most important thing in his life, were almost ready. But he didn't look at the lights and the toys before they went into the bags.

• He didn't wait around to see the presents being opened

He stopped his sleigh at each house and put pretty presents under each Christmas tree. In one house, a little boy came down the stairs and watched him. When Jack turned away from the Christmas tree, he saw the young child. "Here, little boy! A present from Santa!" said Jack. And he gave the boy a present.

Jack had to go to the next house. He couldn't wait and watch the boys face. But when the child opened the present, he didn't smile. His face went white and his mouth fell open. He screamed wildly.
Jack heard the boys screams and he smiled. "He likes it," Jack thought. "Nobody is scared of me and I'm making everybody happy!"

• Mistaking the scream of terror for screams of joy (a natural mistake for the King of Halloween), Jack genuinely believes that he's doing a good job

There was only one happy face in town. High above the police station in a strange sleigh, a skeleton's smile shone. Inside his head were pictures of happy children's faces. He had no idea about the problems below.

As explained, Jack does not truly gets Christmas. Furthermore, even if he saw gifts from Christmas Town, he might just have noticed they are small objects, with fun colors, and which are childish. Nevertheless, as we can see at the beginning, Halloween people are really enjoying frightening things and they are having fun with the creepiest jokes, so they did it as well and it did not surprise Jack at first. That's why he only understands his mistake after he has been taken down by the army (graveyard scene/song "what have I done" <- means "now I realize I did not do it well)

Jack might also have convinced himself while telling Santa is a terrible guy, and thinks to understand that this big boy might like "Halloween Style Xmas"