That is a mirror lens, I personally have never worked on a mirror lens but fungus can be bad or it can be very easy. The risk you take is if the fungus is producing acid which can damage coatings and etch glass. I am not sure how to take a mirror lens apart because I have never worked on one but the main thing you need to concern yourself with is killing the fungus otherwise your cleaning will be for nothing. There are many methods people use, some say saliva is good but I prefer vinegar and water mixture. Depending how bad the fungus is you may want to let the infected glass soak in the vinegar and water for a few hours. Another way to kill fungus is to blast it with UV light but getting UV light strong enough can prove difficult. After killing the fungus I typically use 90% and up rubbing alcohol and Kimwipes(google them, scratch free and lint free) to clean everything, a good airblaster to clean dust from the lens.
The vinegar solution I use is 60% vinegar and 40% water. I like to use standard Q-tips to clean then use the Kimwipes and alcohol to polish up, so to speak
Preventing fungus in the future is as easy as keeping a few bags of silica gel in with your lenses.