We all know that cryptocurrency is a risky investment and it isn't easy to HODL your bitcoin unless you have savings that you could use if you experience problems and badly needed some money. Make sure to only invest money that you could afford to lose on cryptocurrency because if you are not careful you could possibly lose it all if you invest all of your money in cryptocurrency and then you didn't have savings something like health insurance if you needed money if your sick or one of your family members is sick where are you going to get that money your just gonna end up selling your cryptocurrency and probably end up with a lose.
I think in your situation you should use your emergency funds since it's for an emergency, if you use that money you could avoid selling your cryptocurrency assets meaning you're avoiding losing money, but I guess if its a good time to sell and you could make a profit if you sell if you make a decision to sell your cryptocurrency it doesnt matter since you already make a profit another opportunity will come to reinvest your money again on cryptocurrency or other investments.
I believe that it depends a bit on the emergency as well in this situation. Like just this Sunday I was taken to hospital, and I had to get MR scan and all that bells and whistles, in my nation thankfully it is not as expensive as USA so I was fine, but I had to sell just a bit of my bitcoins to pay for that, because I had no money left in either my credit card or debit card to pay for that and survive until the end of the month.
I am fine, just that it was an unexpected stuff and not like I cashed out a lot, I cashed out only what I saved last month, so it wasn't really much big deal at all, it was definitely small detail only. But I had to, and I did, didn't even worried about it, because that's literally why it's there.