Can I use an iPhone like the iPod touch

Yes, you can. There is no requirement for a SIM card in iPhone. I myself used an iPhone for about four years without a SIM card. The only issue is that you need to either find public Wi-Fi or a friend willing to lend you their hotspot.

As pointed out, you will need a sim card for activation.

My only piece of advice, maybe look at refurbished devices so you save some money.

Why not just buy an iPod touch then? Click here-> Buy iPod touch - Apple

With that said, yes, you can use an iPhone like an iPod, but you will need a functional nano sim card for activation, even if it does not have cellular service attached to it. Also note, you’ll be paying much, much more for an iPhone than an iPod.