Question: I already know that pressing `Ctrl` + `W` will hide the bottom part of the HUD.

But how can I hide the rest of the HUD that is shown on the top of the screen and the replay progress bar?

Answer: 
As far as I can see that is not posible, here is a list of what you can do while watching a replay:

> 
> Unit Following - You can lock the camera to any unit to follow it
>  around the map. To do this select the unit and press `Ctrl` +
>  `Shift` + `F`.
> 
> 
> Replay Overlay - An overlay in the top left displays various
>  information for every player as chosen by the viewer. These options
>  are listed below.
> 
> 
> * **N**one - Closes the box.
> * **R**esources - Displays Mineral, Gas and Supply counters.
> * **I**ncome - Displays resource mining over a set period of time and the number of workers.
> * **S**pending - Displays where resources are being spent, either on Economy, Technology or Army.
> * **U**nits - Displays number of units.
> * Units **L**ost - Displays number of lost units.
> * Pro**d**uction - Displays all research, construction and production taking place.
> * **A**rmy - Displays Army units in terms of resource cost and total Supply stats.
> * AP**M** - Displays average and current APM. Due to Game Speed issues, these are currently inaccurate.
> 
> 
> Patch 1.3.0 introduced several new features and Patch 1.3.3 changed
>  the Current APM hotkey. These are listed below:
> 
> 
> * In a 1v1 game, both players’ resource rows are shown in the upper right at the same time.
> * The main game UI can now be hidden/shown by pressing `Ctrl` + `W`.
> * The ability to toggle between player unit colors and team unit colors when watching a replay or observing by pressing `Alt` + `F`.
> * New bigger panels are now available when observing or viewing a replay of 1v1 games. These panels are large and are shown in the top
>  center portion of the screen:
> 	+ Player Name Panel: Displays the players' name, team color, race, and supply count - `Ctrl` + `N`.
> 	+ Current Income: `Ctrl` + `I`.
> 	+ Army and Worker supply: `Ctrl` + `A`.
> 	+ Units and Workers killed: `Ctrl` + `R`.
> 	+ Current APM: `Ctrl` + `V`.
> 
> 
> **Tips**
> 
> 
> * If you've lost a key unit in a game, for example the blue player's [[Banshee]], you may be able to find it by selecting a blue unit and
>  finding it on the control group display. Just double click the control
>  group the Banshee is in and the camera will focus on the units.
> * By holding `V` when having a unit of one player selected your vision will switch to that of the player until you release
>  `V`.
> 
> 
> 

Source: [Liquipedia](http://wiki.teamliquid.net/starcraft2/Replay_Features)
Actually you can with the letter `H`.