Here is a basic tiramisu recipe
that can be done by hand with a wire whisk and a bowl - it will just take a little more (I lie - a LOT more) effort than using an electric mixer. I have made it that way (not this specific recipe but same basic idea) by hand ... gave me a good excuse to buy a cheap ($10-$15) electric hand mixer.
Like Alix said - it sounds like your recipe is using whipped egg whites to lighten the cheese. Whipped cream is not stable enough to do the same job the egg whites will. You can whip egg whites with a bowl and a wire whisk - you just have to use a bowl that is made from metal, glass or ceramic and wipe it down with a little vinegar on a paper towel to make sure there is no grease/oil residue on it; wash the wire whisk well and let sit in a glass of warm water with a little white vinegar in it, too, for 3-4 minutes to make sure it is grease/oil free and rinse with plain water and dry it off before you start - and you CAN NOT use either a plastic bowl or whisk. Then, go to town beating the whites - it does take time and effort. Or, also as Alix suggested, ask a neighbor if you can borrow their hand mixer for a little while.