Chain Compatibility

A 10-speed cassette will take a 10-speed chain. Any 10-speed chain from any chain manufacturer that manufactures Shimano-compatible chains(*) should work. In particular, the CN-4601 should work.

However, do note that the chain needs to be a correct length. Longer is ok as you can always shorten a chain with a chain tool, shorter is not. If it's the correct length, and if it uses a quick link, you can install it without a chain tool. If you need to shorten the chain or if it uses a reinforced connecting pin, you need a chain tool. (Plus you may need a chain tool for removing the old chain in case it doesn't have a quick link -- for quick link the correct tool is pliers.)

For example, I have a bike that has 11-30 tooth 8-speed cassette and 48 tooth big ring, plus 46cm chainstay length. The chainstay is so long it really needs a 116-link chain. A 114-link chain won't work. Also I can't switch to a 11-32 tooth 8-speed cassette or a 50 tooth big ring if I want to continue using 116-link chains.

(*): The original version of this answer told any 10-speed chain will work, but later I was told that Campagnolo 10-speed chains are slightly wider and thus could have less than optimal shifting. There are many brands making Shimano-compatible 10-speed chains such as Shimano, SRAM and KMC. It doesn't matter whether you use symmetric or asymmetric or HG-X or non-HG-X Shimano chain. I have a HG-X Shimano chain on my road bike and it works just fine, so certainly HG-X is not "MTB only".

CN-4601 is one of the asymmetric Shimano road 10 chains. It won't play nice with a triple. You haven't provided sufficient information. In other words if you have FC-4600 or some other double, yes, but if you have FC-4603 or some other triple, no.