Translation:How should we cut the cheese without a cheese slicer?
Good question. It wouldn't really be idiomatic Swedish to add en here. If we look at sentences without a negation first, we often use 'instruments' without an article. For instance skära med kniv 'cut with a knife'. You can say skära med en kniv too, but that sort of individualizes the instrument in a way that in many cases isn't necessary. So skära med kniv is a bit more general and places less focus on the specific instrument.
Some examples might help:
* Hon tog en kniv och skar upp brödet 'She took a knife and cut the bread' <-- en is totally necessary
* Hon skivade brödet med en stor röd kniv 'She sliced the bread with a big red knife' <-- en is totally necessary
* Det här brödet är för hårt för att skära med kniv 'This bread is too hard to cut with a knife' <-- adding en sounds a bit off
* Han brukade skära osten med (en) kniv 'He used to cut the cheese with a knife' <-- if you have en in it, he probably used the same knife at all occasions, but without en, he just cut it with a knife, some knife, whichever one.
In a negated sentence like this one, in Swedish, as opposed to English, it would be perfectly OK to say någon here. In English, any doesn't sound so good with concrete singular nouns, so since you don't want to say without any cheese slicer, you say without a cheese slicer instead.