12V would be in line with many things, should power the amp and is a common voltage to boot. If you have a 120V transformer and the player still works then measure away, far nicer than counting turns or any of the other methods.
Some motors change in speed depending upon the frequency you put in. In some legacy gear it will mean the motor spinning the record/reel/whatever runs accordingly faster or slower (and a really noticeable 12% or so for 50Hz to 60) and that will have a knock on effect to the resulting music (I don't know if you watch techmoan on youtube but the magnetic wire audio player he had the other month was a good example of this). If you are really bothered you can make arbitrary frequencies, the main device to do it is called a VFD (variable frequency drive) and machinists use them all the time rather than changing gears on their tools. However they are not ideal for some audio gear. There are even older things (various generators and rotary phase converters) but don't go there if you can avoid it.
From the specs I saw the thing is rectified and smoothed before it does anything in it. The only way I can see it troubling things here is if the circuit was not smoothed enough by the capacitor and the ripple was the timer but that is really quite silly, or if again it is not smoothed fully and something about duty cycle and heat dissipation.
You don't need the same VA/power rating, don't go lower unless you are sure but you can go higher if you want and that is all the shop has/has for a decent price*. Whether you can wedge it into the case is a different matter and I think one of the smoothing capacitors was attached to it but that is neither here nor there, and while I have not pulled it apart going by the exploded diagram there should be a bit of wiggle room.
If you really wanted you could probably chop out the transformer and rectifier (maybe leave the smoothing cap) and stick a wall wart/switch mode supply in there (12V and next to no Amps is easy to find). They can be a bit noisy, especially modern switch mode stuff, but try if you like.
Had the transformer been some kind of crazy multi tap thing that generated 10 different voltages, parts of the thing used AC and so on and so on then yeah trying to find a generic replacement would be hard. This is an absolutely basic, first principles transformer doing a common voltage and not gobbling a lot of power by the sounds of things. If you want to use denon stuff, and it will likely bolt straight on, then go for it.
*
https://www.rapidonline.com/vigortronix-vtx-120-003-612-pcb-open-mains-transformer-3va-0-12v-88-3702 has one that will do (you will have to jump the middle pins as it is designed for 120 and 240V, like I imagine Denon would have done in the first place like every other manufacturer for the past 20 years) for a whole £2.85 plus VAT and shipping (or nothing if you live anywhere near Colchester and can get to their shop). I don't know what maplin will have and I would rather not spoil a good evening by fighting with their site. The cable is just a cable so use whatever you like, do make sure to earth it if there are external metal parts that could become live.
I don't know why the case and parts are different between the runs, I could speculate, and that would also lead me to wonder why it was not a universal transformer and regulator setup, but were I a betting type I would go with no effect on resulting audio.
As for why denon reps said don't do it then I am going with they either want to sell you something or they are covering their arses -- they might well have other models on the market with a drive that does need set frequencies and can't be bothered to look it up or risk telling you the wrong thing.
