We placed our tile in mortar using the recommended tool and it squished up higher than intended and dried in the grooves of the tile sides because I ended up in the ER at the time it was supposed to be cleaned out. We have been trying to scrape mortar out of the mosaic tiles but it is extremely difficult. We thought about options, ie. Scraping mortar, ( how best to do so, I don't know. The tiles are as small as 3/4 inch, a daunting task), using a tile sealing caulk in place of grout since there is not much grout, tearing the whole thing out and starting over(the least desirable. Suggestions?
This happens on every tile install at least a little. There's nothing wrong with some mortar squishing out. Now, if it's over the top of the tiles, that's another issue. If you think there's room for a caulking/grouted/sealant, then there's likely room for grout.
You can use a sealant in place of grout, but from my experience having done this before, the sealant attracts dirt which seems to stick to it vs. grout where you can just sweep dirt off your tiles. Also, the sealant is less durable to foot traffic and wear and it's a huge pain to put in.
Grout is just colored/sanded cement. It will adhere to your mortar that is already there. No one will be able to tell unless maybe you want white grout and your mortar is grey. I'd just use grout anyway and see how well it covers. And if you really think you need to remove some of the mortar from between tiles, you will make your life a lot easier by using a multi-tool with the proper vibrating blade attachment which is made for masonry. You can get a carbide masonry blade that will fit most of the common multi-tools. It's meant for grout removal, but it may help a lot for your situation as well if the mortar is sticking up really high.
When you lie the tiles in a mortar generally speaking it is better quality; but when something goes wrong, like in your case problem is much bigger than it would be if you have just used a glue.Celaning splashed mortar of the tiles is REALLY hard, and plus you will most likely damage (scratch) your beautiful new tiles. Try using soft sponge and water and rub until your hands bleed :) but there is no guarantee. When it comes to sealing space between tiles (fugues) I don't see why not using grout or sealing caulk or products which are specialized for this purpose. If tiles are outside best would be to apply old technique: use fine mortar (cement and extra fine sand) that's how people did it in the old days before new materials. Now if your tiles aren't flat (horizontal on the floor and/or vertical at the walls) if there are "waves" I recommend that you replace them, or maybe you decide that it is acceptable and learn to live with it.