I wouldn't worry about delays on an April morning - it is highly unlikely (although not impossible) that there would be severe weather at this time of year.
What do you mean by tickets not being available? I could find some advanced fares at £37 each way - although most of them have gone already. Do a search for London to Nottingham for these. In fact, the 11.10 from Kings Cross, changing at Peterborough is currently £24 for First Class. Such are the stupid ways in which our train system runs.
Your greatest threat is engineering works on the lines - there are indications that you'll suffer these on the southbound trip.
Heathrow Connect is your best option - slightly slower than Heathrow Express, but far cheaper.
If you turn up on the day to pay, you will be 'taken to the cleaners' by our rail industry.