Its not especially difficult (I managed!), however it depends if you have all the "bits" you need whether the £300 is actually a good price or an average price. I'm assuming you are talking about an engine which is set up for remotes already (if it is configured for tiller steering its likely to need some bits to set it up for remote).
(1) Fit the steering cable (I'm assuming its cable steering not some weird ancient rope steering or hydraulics found on bigger boats). You may need a new cable if the old one is missing or difficult to move. At the helm end, IIRC it is just a case of feeding in the cable as you turn the wheel and then doing up a big nut (inevitably this will be in a really tight awkward sport that only lets you turn the one spanner you have the right size 1/12th of a turn at a time! At the other end the "bar" part of the piston goes through the tilt tube on the outboard and another couple of big nuts get done up. There is then a shaped piece of steel bar which connects this to the front of the outboard - again if you don't have these it will cost for manufacurer original parts. [note i've assumed to fit the steering "piston" to the outboard you need the engine off the transom to get enough clearance (I do) but the length of cable means you need the engine very close to the boat to get it all together which means you need some sort of stand / hoist. You can probably fit the engine end first - but if there is already a cable fitted then you might want to leave the helm end connected?]. Cable needs to be just the right size and routed wherever you want it to go.
(2) Fit the engine to the transom. This is probably the scariest part as except for very small engines means drilling holes in the transom (if you are replacing another engine then there might already be holes in the right place). Make sure you seal holes you drill properly. You may need to buy the bolts (which will be more than you expect!). If there are no existing holes then search here and google for advice on height. I'd guess that you don't need any "offset" from the centreline on a 4m boat but you might want to research this point.
(3) Fit the throttle and gear remote cables - depending on the engine and controls nothing more than some screws and clips - but you need to adjust to the right length (jf they are wrong you may be stuck in gear which is quite alarming when you start the engine shoot forward, then try to reverse to slow the boat down only to discover that your "blast of reverse" is actually an extra blast of forward - don't ask how I know!). Nothing too difficult, can be a bit footery, especially if you are trying to route them / round through any ducts. You may need new cables (more cost). Again they need to be the right length.
(4) Connect any electrics (power trim, kill cord, ignition key, tacho etc). Could be as simple as plugging one big socket into another - but unless they were similar engines it is unlikely! You could have quite a few crimp / solder connections to bugger about with. Nothing major but those little jobs, and sealing it all up always take longer than you think.
(5) Connect the battery, which may include fitting a battery, battery box, isolator switch etc.
(6) Test it all - and debug any issues!
If you were an outboard engineer rigging a brand new boat with brand new kit then it would probably only take half a day. If its your first time, and you are dealing with old bits of kit that need some effort then its definitely a whole day, and possibly a whole weekend of work - but nothing which is particularly skilled. Beware you could easily spend £150 just on the bits and pieces you need to stick a random second hand engine on a random second hand hull/console.