I wouldn't bother with the disposable phones on the tables - they're expensive to buy and develop and often come back with rubbish pictures.
Instead...
Do any of the guests particularly like taking photos and/or are they any good? I would ask a couple of guests (one on each side, plus maybe a couple of friends who would between them know who lots of the guests are) to be your photographers and ask them to try to ensure that they get at least a couple of pictures of each member of the family/all the friends.
Talk to them about this in advance so that they can be prepared and make sure they have plenty of space on their memory cards/phones and a fully charged battery. It might also mean that somebody will bring along a dslr rather than not bother.
Work out if there are any particular shots you want - of you as a couple, individuals, family groups etc - make a list and make sure that you have several copies of it. Ask those taking the pix if they would help you do these pix and get someone like the best man or an usher (or equivalent if you're not having them formally do the role!) as a designated person to collect up people for the photos when you're doing them. Aim for some at the registry office and then if you miss any, or you want a second set of everything in case they're better, then you can still try again at the party. have a little announcement to this effect at the registry office (they often do a little 'notices' type announcement about what's happening next at the end, making sure that everyone has lifts, taking flowers with you and so on, so include in that so the photo sessions, albeit brief, won't be a surprise and you won't all be waiting for auntie maude who has wandered off to inspect the flowers next door)
If there is anybody there on their own or who won't know many people, asking them to take a photo of everyone can be quite a good way for them to meet people with no pressure - gives them a reason to talk to people, to interact briefly and disappear off again...
Lots of people will have mobiles that will take great pictures so again, actively ask people to take picture and have the link to send them to you after the event. If you have techy friends, there might be somebody who would be happy to take a laptop and download the evening's photos at the event.
IF you're having tables, put a list of photo/video challenges on each table - some 'serious' best pictures of the bride/groom/couple/family/food/cake/ring/venue/etc - but also silliest face, selfie with the most people in, funniest captured moment, sloppiest kiss, wildest dance move, most unexpected moment and so on. Offer prizes for some of the most memorable pictures of the event that really capture it for you (I'm thinking tiny or fun prizes, so a bag of haribo or a freddy frog chocolate bar rather than anything expensive) to encourage people to have a go.
One other thing to try - ask a local photography group or course if there are any keen amateurs or students that would be able to take pictures for you - even if just for the registry office or an hour at the party - for a minimal fee (what would you have spent on disposable cameras?) and the chance to have a go at photographing a real wedding, that you would let them use for their portfolio and provide a reference. You might find that there are no takers but sometimes it can be very difficult for people to get that first booking to become a wedding photographer so they might be up for it. I know a couple of people who started like this - basically did it for petrol costs and their food - as they needed those all important pictures to show to clients that they could do it. If you don't ask - you definitely won't get someone. If you do ask - there's a chance that you might find someone...
[Apologies if I have cross posted with anyone, I started writing this a couple of hours ago and got pulled away - but thought I would post anyway]
Anyhow, hope you have a lovely wedding and a wonderful marriage afterwards! 