Ca my newborn sleep safely in a bassinet ?

So we have a crib but we have to order a new mattress tomorrow and I’m already 38 weeks so I’m guessing he will be here before the mattress gets here. So our plan was to get a bassinet for him to sleep in in the meantime. Is that safe for night time sleep too ?

We have a nice co sleeper that attaches to our bed that we used for our daughter when she was born but it makes me nervous bc our daughter is 18m and she still sleeps in bed with us and I don’t want to risk her waking up in middle of the night and like grabbing him or throwing a blanket or stuffed animal on him. Idk it just makes me too nervous.