You probably can do some of the skills at the emergency hospital, just not all of them. When your externship paperwork opens, there will be a specific list of both skills and equipment needed. You just have to submit paperwork for each hospital specifying which skills you will be doing at each one. Also, someone will have to be taking pictures/video of you performing said skills, so that factors into how busy a place is and whether someone is available to do that. You'll have to calculate your schedule rather carefully to fit everything in, I would guess. I have heard of students who have taken vacation or some days off to focus exclusively on skills, if that's a option for you.
I'm sorry I can't be of more help to you, I work at a vet hospital so I did all my skills there, both during working hours but also on my days off for things I don't normally do, like answer phones and make appointments. I hope someone who like, you doesn't yet work for a hospital, can give you better strategies.