Hi DazedandConfused254,
If I remember to, I'll actually plan in advance what my approach will be regarding beggars. If I have some spare coins I will bring those to give but if I have nothing to contribute or just don't want to for whatever reason, I just look at them and say, 'no, sorry' and carry on walking - that should be enough. But if one of them wants to give you an explanation as to why they're asking for money, just say, 'sorry I have to go' and keep walking.
Yes, I find the whole thing awkward myself, but I find interactions with all strangers awkward. One beggar approached me though, and I stopped, and he asked me for $10 - petrol for his car. I actually laughed, haha. I don't know why.