I had a similar situation - I just sent a quick note
'Please don't take this the wrong way - I just wanted to acknowledge your loss at this time, I wanted to pay my respects and offer my help if you need anything'
I thought I'd throw this out there... I used to start my one-way communications with some form of "disclaimer" like i highlighted above... I've stopped doing that as I felt it came off as controlling and/or manipulative.
On qt4's post, it's perfect alone, without the disclaimer in front, "I'm so sorry for your loss... If you need anything at all I'm here... etc" Direct, caring, and meaningful.
I stay away these disclaimer type intro's to one-way communication. After enough of this no-nonsense approach, my W has actually come around and started telling me she doesn't think I'm lying about everything anymore. She believe the things I say, and it's because I don't provide these long, drawn-out excuses, reasons, and disclaimers about why I'm NOT lying anymore.
Thoughtful, Truthful, Direct, Consistent. Enough of this, no disclaimer will be needed again.