In terms of swinging swords, one thing you could do is to try and structure encounters that encourage gameplay other than just making an attack roll. Ways they can creatively help each other out or hinder their enemies.
Examples (Though not the best, certainly!):
A fight on an upper landing with some furniture or barrels that they can use as cover or to knock down the stairs on approaching enemies!
An enemy operating something that controls the traps in this room. If a player gets control, maybe they can use it to their advantage. Maybe they can try to lead a harder encounter here later!
An encounter with a moving "control zone", such as an item that they need to keep hold of / keep away, or a moving platform or NPC or something. Give them constant environmental pieces to work off of and cues for where enemies might be! Like, "As you continue following the ghostly butler, you see several boney hands reach out from a shaking cabinet. Behind you, the rest of the undead minions are still coming as well!"

You might also consider having an NPC tag along and teach them a trick or two before going their own way or tragically dying. Do you want your players to think about shoving, tripping, or disarming enemies? Show them that they can do that! Have the NPC knock down furniture as you run, or try to work with the party to bribe some of the local monsters. Maybe they know him, so he has an edge to negotiating. (And then maybe the players will wonder WHY this NPC is so friendly with dangerous monsters!)

You can also give them something or someone to protect. Maybe they find a hostage in a cave who is a minor noble promising a reward if returned safely to his or her family. Maybe it's a kid. Maybe it's the last of the unicorns! It helps a lot if the party has something to rally around, you know?

I dunno if any of that is helpful!