As an avid side saddle rider, I can tell you without a doubt that riding in a western saddle will accomplish what you want in general but you are going to be in a ton of pain and very out of whack in your position. It will not look right at all. Your leg will kill you not only from the horn's position but the angle which it must be held at which will cause your body to lean forward thus making you look not so pretty. Not what you want on your wedding day.
I would NEVER ride sideways (especially in a slippery wedding dress) on an English saddle unless it were an English side saddle. You will slip and then you will not be able to get your other foot out of the stirrup. I would not even do this if someone were leading the horse.
Not only do I ride all three seats side saddle (English ~ Saddle Seat, English ~ Hunter and Dressage, and Western ~ Stock Seat), I also am a competitive jumper while riding side saddle. A side saddle is balance for you to ride on the side and it is literally possible to do just about anything that you can do astride (regular saddle) in it.
I have found many side saddles around your area, if you are in deed in Cairns, Queensland, and will list them further down. It is important that no matter what you do (I also ride in period costumes which are often noisy like a wedding dress and full like one as well), that you practice many times with the veil, holding a fake bouquet, and in the dress on the horse. Even if it is walking around an arena for a few laps to make sure that the horse that you are using will be ok with it.
This is something that most people do not do, and then we watch the after results on the wedding nightmares television shows. You do not want to end up on there. The other factor which you will need to take into consideration is the wind which you will have at the beach. This wind will be anywhere from easy to hard depending on which direction it is coming from. I do not know which type of wind (northeasterly and all the others) is worse for your area. Always plan for the worst. Figure out how it will affect your dress by blowing it into the horse, blowing it up into your face (veil included on this one), and then make a plan to keep it from happening. On every side saddle habit (both regular modern show and the period costumes) I have weights sewn into the skirts all around it to keep it down. The type of weights which I use are the curtain weights which are round and are designed to be sewn in. You can even glue them in if needed. This will keep the dress in place and reduce the movement which you have.
Your veil can be pinned to your dress in order to keep it in place. I wear a lot of different hats and some of them either have large ribbons or netting coming off the back of them much like a veil. It is important to pin them down so that the wind and speed of the horse does not cause it to fly into your face where you cannot see or even worse standing up straight for pictures.
Always think of the worst possible situation ahead of time and make adjustments to your dress and accessories to plan for it. This along with practice will help your wedding day go off without a hitch. If you are not used to horses, you need to take some lesson prior to doing so, but I think that you are since you are asking this question in the manner which you are.
As for the side saddle, if the horse is not a side saddle horse (and there are some which are not), it is going to take time to train them to it as not every horse is easy and relaxed with one. You will have a balance girth/cinch (depending if it is western or english) which will be TIGHT to keep the saddle from moving about. It is hard even on a side saddle to keep it in the center since all of your weight is on one side. This can sometimes make horses not used to it a bucking nightmare. The plus is that it is almost impossible to be unseated from a side saddle as you are very secure in your seat with having the two horns (leaping horn) which your legs are able to squeeze very tightly. Western side saddles do not always have this, but I have seen some that have been made with two horns versus just one. Most commercially (not custom) made ones only have one horn for your legs which is a less secure seat.
You have to get one which is going to fit you as well. To do this sit on the side of a chair in a position similar to a side saddle position. Basically your right leg will be propped up on the arm of the chair from your hip to your knee. Then measure from your hip (where it contacts in your seat) to your knee. This measurement since you are an adult will be somewhere most likely in the 19 to 23" length. I am not sure if the measurements there for side saddles are done in cm or inches, but it is only a simple conversion.
Next, your dress as you are getting up on the horse needs to be picked up to your waist (so where some shorts or something you do not mind the rest of the world seeing under it). When