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You look around the hallways. Apart from the extra-large control center, the network version of the Hospital is a replica. You can use the same map and make your way to the surgery room. However, you'll likely run into plenty of Digimon as a group, and have to evade or defeat them in turn. Maybe you can find some kind of alternate approach that's less risky. You've already done a good job of mitigating said risks, might as well keep it up.
>Don't try anything new. Sneak straight for the operating theatre that Pulsemon last saw Cutemon and the kidnappers in. You have a set goal in mind, just go straight for it and endure the patrols as you intended. You've trained Phascomon to do exactly this, so the main risk is Ryan, Pulsemon, and Gizamon bumbling along.
>Send Pulsemon all the way to the surgery room to scout first. Find a safe corner to camp out. In the meantime, you can do some passive exploration of your surrounding area or chat with Ryan. Once he's back with confirmation that it's the right place, then you can move out.
>Instead of going there, head out of the window and wander the outer grounds. Pulsemon said he was worried they'd move Cutemon soon. They have nowhere to go but out into the Network if so. You can just camp out by the exit point and wait, eliminating the drawback of your companions being less stealthy than you. It's a practical move, but you won't know what's happening elsewhere while you do it, and Pulsemon will probably be too antsy to sit still while you bide your time.