Go to bed at 8pm and your DP can do the last feed. You then get a decent stretch from 8pm to 2am...
Do 4 week old babies have a last feed? I know when mine was 4 weeks old he cluster fed from 8pm until about 2.30am....
But as others have said - why are trying to wake a sleeping baby? Has it been recommended to you by the HV due to poor weight?
My husband was brilliant with both our babies in that he would always support me during the night. I really struggled with the 5-6 hour cluster feeding sessions and my DH would stay awake to make sure I didn’t fall asleep holding the baby. The cluster feeding ended when the baby was about 8 weeks old and even then my husband would still get up when the baby woke and he’d do the happy change before handing me the baby to feed. He would then go back to sleep which was fine by me as he’d done his part. In the early days I used to tell him all the time to go to the spare room, to get some sleep etc but he never would and would instead be sitting up with me watching box sets whilst I was feeding. He would tell me that it was our baby and we were in it together. Every night when he cane home from work he would take the baby and then send me to bed for two hours.
Our oldest son is 4.5 years old now and our youngest is 16 months and still breast fed. He’s a horrendous sleeper and is still up 2-3 times a night. My DH sleeps in the spare room as me and the baby co-sleep but when he’s woken by the baby crying he will always come in and check I’m okay and if there’s anything he can do. If the baby wakes up for the day any time before 6am then DH will come and get him so I can have a few hours more sleep.
Since the birth of the first son I have always had Saturday and Sunday lie-ins because DH will get up with the boys.
People say not to do competitive tiredness but thankfully my DH has always said that he knows I’m more tired than him so he does as much as he can to help.
Seeing as your partner is off over Christmas he should definitely be helping you out more around the house and taking the baby to give you breaks. Even if you aren’t getting breaks to sleep it will still be invaluable for you to just have an hours hideaway upstairs to read a book, watch some telly etc just to have some time to yourself.
In answer to your question, I don’t think you’re being unreasonable to expect help overnight when your baby is so young, even if your partner is at work. A general view is that if a woman is BF’ing a man is working then of course he should have a nice 8-10 hours unbroken sleep each night whilst his partner is up all night exhausted caring for the baby....... 
It’s not a view I hold though and he needs to step up and help parent the baby. Babies are 24/7 hard work and if you dont get to clock off during the night then neither should he.
The first few months are horrendous and team work is imperative and you need to feel that you’re in it together, not in it alone whilst your partner sleeps 