You have two options: (1) quit or (2) "renegotiate the relationship", as the saying goes.

Specifically, it's perfectly reasonable for you to say "OK -- if you're willing to provide me with a dedicated laptop". They can say no of course, but so can you. Or you can request a rate increase (which they would probably say no to, if they won't provide you with a laptop).

Either way, those are you choices. Yes it sucks to a degree, but that's what work does generally and which is why it pays money. All we can do is moderate the suckiness-to-money ratio as best we can.

My client is quite reasonable, and is willing to compensate a new laptop.

It took me less then a few minutes after I read the mail to come up with algorithms to implement this thing without compromising my security or privacy. VM. Using an old laptop and remove the wi-fi card. Get a new PC or laptop. Wire whatever I choose on a vlan that goes directly to a VPN server in another country.

However, I still don't like the idea of running an agent on my/a machine. It's a road I feel strongly against going down. But then, I came from a different time, when people still trusted each other and acted in good faith.