@Jan Atom The answer depends on where you want to take your hi-fi in the longer term. If you are happy with the sound of your current system, the problem is in its likely longevity more than the need for immediate change.
Unsurprisingly, as it is now a decade since Linn gave up making CD players, they no longer support any of their CD models. Your laser upgrade was probably a very good investment, as that seems to be the part that gives most trouble. From my experience and reports on the old Linn forum, people tend to have more trouble with the CD transports than the CD electronics, so a new, separate DAC is not necessarily the best bit of future proofing for your current system.
I faced this same problem some six years ago (though by then my Linn Mimik had been replaced with a Roksan Kandy Mk. III, which I still have). In the end I bit the bullet and went the streaming route with an ADSM (costing me, of course, far more than €500). The CD player was (and still is, despite other system changes) digitally connected to my DSM, and so, in effect, had its DAC substantially upgraded. So I still had full access to my CD collection while it was still being progressively ripped to the server for streaming purposes. These days, there is another option for DSM owners who don't enjoy ripping and tagging CDs (I do); leave the CD collection and player as they are and use them as before, while also subscribing to one or more of the streaming services.
Frankly, if €500 really is the total budget, I'd be inclined to hold on to what you have and put the money into an upgrade fund for the day when you finally lose the Karik. Tim is correct in saying that newer DACs are far superior to those of a decade ago (and streamers generally perform better than CD players), but the Dragonfly that he mentions (I have one) is a USB device, so very different from what you are running now. If CnoEvil is correct, and you can get a Sneaky DSM (rather than the DS, as you will want to connect the Karik) within budget, that would certainly be an option. But you might well find that future proofing with longer term satisfaction is only achievable, with any make of kit, at a much higher price than your current budget.
David